{"id":13671,"date":"2021-04-12T15:51:24","date_gmt":"2021-04-12T10:21:24","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=13671"},"modified":"2022-02-24T08:12:16","modified_gmt":"2022-02-24T02:42:16","slug":"04-04-00-3","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/04-04-00-3\/","title":{"rendered":"04.04.00 – \u0d85\u0dc4\u0db6\u0dd4 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2 \u0daf\u0dd9\u0d9a\u0d9a \u0dc4\u0ddd \u0dc0\u0dd0\u0da9\u0dd2 \u0d9c\u0dab\u0db1\u0d9a \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0d9a\u0dca\u0dad\u0dad\u0dcf\u0dc0"},"content":{"rendered":"\n
\n
\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n

\u0dc3\u0d82\u200d\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0d9c\u0dab\u0dd2\u0dad\u0dba II ( \u0dc0\u0dca\u200d\u0dba\u0dc0\u0dc4\u0dcf\u0dbb\u0dd2\u0d9a \u0d9c\u0dab\u0dd2\u0dad\u0dba ) \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dad\u0dca\u200d\u0dbb\u0dba\u0dda A \u0d9a\u0ddc\u0da7\u0dc3\u0dda \u0dbd\u0d9a\u0dd4\u0dab\u0dd4 25\u0d9a \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0\u0d9a\u0dca \u0db8\u0dd9\u0db1\u0dca\u0db8 \u0db8\u0dd9\u0db8 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad\u0dc0\u0dbd\u0dd2\u0db1\u0dca \u0d87\u0dad\u0dd4\u0dc5\u0dad\u0dca \u0d9a\u0dbb \u0d87\u0dad.<\/span><\/strong><\/p>\n\n\n\n

\u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2<\/strong><\/strong><\/h3>\n\n\n\n

\u0dba\u0db8\u0dca \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2\u0dba\u0d9a \u0dc3\u0dd2\u0daf\u0dd4\u0dc0\u0dd3\u0db8\u0da7 \u0dc4\u0ddd \u0dc3\u0dd2\u0daf\u0dd4 \u0db1\u0ddc\u0dc0\u0dd3\u0db8 \u0d9a\u0dd9\u0dbb\u0dd9\u0dc4\u0dd2 \u0dc0\u0dd9\u0db1\u0dad\u0dca \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2\u0dba\u0d9a \u0dc3\u0dd2\u0daf\u0dd4\u0dc0\u0dd3\u0db8\u0da7 \u0db6\u0dbd\u0db4\u0dd1\u0db8\u0d9a\u0dca \u0db1\u0ddc\u0d9a\u0dbb\u0dba\u0dd2 \u0db1\u0db8\u0dca, \u0d91\u0db8 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd3\u0db1\u0dca \u0daf\u0dd9\u0d9a \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dba\u0dd0\u0dba\u0dd2 \u0d9a\u0dd2\u0dba\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dda.<\/p>\n\n\n\n

A \u0dc4\u0dcf B \u0dba\u0db1\u0dd4 P(B) \u203a 0 \u0dc0\u0db1 \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0dc0\u0dd6 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2 \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0db1\u0db8\u0dca, P (A \u2229 B) = P(A). P(B) \u0dc0\u0db1\u0dc0\u0dd2\u0da7 A \u0dc4\u0dcf B \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2 \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dba\u0dd0\u0dba\u0dd2 \u0d9a\u0dd2\u0dba\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dda.<\/p>\n\n\n\n

\u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2\u0dc0\u0dbd \u0dc3\u0db8\u0dca\u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dcf\u0dc0\u0dba<\/span><\/strong><\/p>\n\n\n\n

\u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd3\u0db8 \u0d85\u0db1\u0dd4\u0dc0,<\/p>\n\n\n\n

P(A\/B) = \\frac{P(A\\cap B)}{P(B)}<\/span> \u0dc0\u0dda.<\/p>\n\n\n\n

A \u0dc4\u0dcf B \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2 \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0db1\u0dc0\u0dd2\u0da7<\/p>\n\n\n\n

P(A\\cap <\/span>B) = P(A) . P(B) \u0dc0\u0dda.<\/p>\n\n\n\n

\u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd3\u0db8; P(A\u2229B) = P(A) . P(B) \u0db1\u0db8\u0dca \u0db8 \u0db4\u0db8\u0dab\u0d9a\u0dca A \u0dc3\u0dc4 B \u0dba\u0db1\u0dd4 A <\/em>\u0dc4\u0dd2 \u0dc0\u0dd6 \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd3\u0db1\u0dca \u0dba\u0dd0\u0dba\u0dd2 \u0d9a\u0dd2\u0dba\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dda.<\/p>\n\n\n\n

\u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2 \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3 \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba<\/span><\/strong><\/p>\n\n\n\n

\u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba; A \u0dc4\u0dcf B \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0db1\u0dc0\u0dd2\u0da7,<\/p>\n\n\n\n

  1. A \u0dc4\u0dcf B1<\/sup><\/li>
  2. A1 <\/sup>\u0dc4\u0dcf B<\/li>
  3. A1 <\/sup>\u0dc4\u0dcf B1<\/sup><\/li><\/ol>\n\n\n\n

    \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2\u0db1\u0dca \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dda.<\/p>\n\n\n\n

    1. P(A\\cap<\/span>B1<\/sup>)<\/li><\/ol>\n\n\n\n

      = P(A) \u2013 P(A\\cap<\/span>B)<\/p>\n\n\n\n

      = P(A) \u2013 P(A).P(B)<\/p>\n\n\n\n

      = P(A) [ 1 \u2013 P(B) ]<\/p>\n\n\n\n

      = P(A).P(B)<\/p>\n\n\n\n

      \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf A \u0dc4\u0dcf B1 <\/sup>\u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dda.<\/p>\n\n\n\n

      2. P(A1<\/sup>\\cap<\/span>B)<\/p>\n\n\n\n

      = P(B) \u2013 P(A\\cap<\/span>B)<\/p>\n\n\n\n

      = P(B) \u2013 P(A).P(B)<\/p>\n\n\n\n

      = P(B) [ 1 \u2013 P(A) ]<\/p>\n\n\n\n

      = P(B).P(A1<\/sup>)<\/p>\n\n\n\n

      \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf A1 <\/sup>\u0dc4\u0dcf B \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dda.<\/p>\n\n\n\n

      3. P(A1<\/sup>\\cap<\/span>B1<\/sup>)<\/p>\n\n\n\n

      = P(A\\cup<\/span>B)1<\/sup><\/p>\n\n\n\n

      = 1 \u2013 P(A\\cup<\/span>B)<\/p>\n\n\n\n

      = 1 \u2013 [ P(A) + P(B) \u2013 P(A\\cap<\/span>B) ]<\/p>\n\n\n\n

      = 1 \u2013 P(A) \u2013 P(B) + P(A).P(B)<\/p>\n\n\n\n

      = [ 1 \u2013 P(A) ] \u2013 P(B) [ 1 \u2013 P(A) ]<\/p>\n\n\n\n

      = [ 1 \u2013 P(A) ] [ 1 \u2013 P(B) ]<\/p>\n\n\n\n

      = P(A1<\/sup>).P(B1<\/sup>)<\/p>\n\n\n\n

      \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf A1 <\/sup>\u0dc4\u0dcf B1 <\/sup>\u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dda.<\/p>\n\n\n\n

      A, B \u0dc4\u0dcf C \u0dba\u0db1\u0dd4 A <\/em>\u0dc4\u0dd2 \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2\u0db1\u0dca \u0dad\u0dd4\u0db1\u0d9a\u0dca \u0dc0\u0db1\u0dc0\u0dd2\u0da7, P(A\\cap<\/span>B\\cap<\/span>C) = P(A).P(B).P(C) \u0dc0\u0dda.<\/p>\n\n\n\n

      P(A\\cap<\/span>B\\cap<\/span>C)<\/p>\n\n\n\n

       = P(A).P(D) [A,B,C \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca A , D \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dda ]<\/p>\n\n\n\n

      = P(A). [ P(B\\cap<\/span>C) ]<\/p>\n\n\n\n

      = P(A).P(B).P(C)<\/p>\n\n\n\n

      \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf A,B \u0dc4\u0dcf C \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dda.<\/p>\n\n\n\n

             4.    A \u0dc4\u0dcf B \u0dba\u0db1\u0dd4 \u03a9 \u0db1\u0dd2\u0dba\u0dd0\u0db0\u0dd2 \u0d85\u0dc0\u0d9a\u0dcf\u0dc1\u0dba\u0d9a \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd3\u0db1\u0dca 2\u0d9a\u0dca \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4. \u0dc3\u0dd4\u0db4\u0dd4\u0dbb\u0dd4\u0daf\u0dd4 \u0d85\u0d82\u0d9a\u0db1\u0dba\u0dd9\u0db1\u0dca, P(A \u222a B) = \\frac45<\/span> , <\/p>\n\n\n\n

                    P(A’ \u222a B’) = \\frac56<\/span>  \u0dc4\u0dcf P(B\/A) = \\frac14<\/span> \u0db6\u0dc0 \u0daf\u0dd3 \u0d87\u0dad. P(A) \u0dc4\u0dcf P(B) \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

                                            P(A’ \u222a B’) = P(A \u222a B)’<\/p>\n\n\n\n

                                                        \\frac56<\/span> = 1 –  P(A \u2229 B)<\/p>\n\n\n\n

                                           P(A \u2229 B) = \\frac16<\/span> <\/p>\n\n\n\n

                                 P(B\/A) = \\frac{P(A\\cap B)}{P(B)}<\/span><\/p>\n\n\n\n

                                    \\frac14<\/span> = \\frac1{6P(B)}<\/span><\/p>\n\n\n\n

                                         P(B) =\\frac23<\/span><\/p>\n\n\n\n

                             P(A) + P(B) = P(A \u2229 B) + P(A \u222a B)<\/p>\n\n\n\n

                                      P(A) + \\frac23<\/span> = \\frac16<\/span> + \\frac45<\/span><\/p>\n\n\n\n

                                       P(A) = \\frac{5+24-20}{30}<\/span><\/p>\n\n\n\n

                                       P(A) = \\frac3{10}<\/span><\/p>\n\n\n\n

              5. A \u0dc4\u0dcf B \u0dba\u0db1\u0dd4 S \u0db1\u0dd2\u0dba\u0dd0\u0db0\u0dd2 \u0d85\u0dc0\u0d9a\u0dcf\u0dc1\u0dba\u0d9a \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2 2\u0d9a\u0dca \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4. \u0dc3\u0dd4\u0db4\u0dd4\u0dbb\u0dd4\u0daf\u0dd4 \u0d85\u0d82\u0d9a\u0db1\u0dba\u0dd9\u0db1\u0dca, P(A) =\\frac13<\/span> , <\/p>\n\n\n\n

                 P(B) = \\frac14<\/span> \u0dc4\u0dcf P(A \u2229 B) = \\frac16<\/span> \u0dc0\u0dda. P(A\/B’) , P(A’ \u2229 B’) \u0dc4\u0dcf P(B’\/A’) \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1. \u0db8\u0dd9\u0dc4\u0dd2 A’ \u0dc4\u0dcf B’ <\/p>\n\n\n\n

                   \u0db8\u0d9f\u0dd2\u0db1\u0dca \u0db4\u0dd2\u0dc5\u0dd2\u0dc0\u0dd9\u0dc5\u0dd2\u0db1\u0dca A \u0dc4\u0dcf B \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2\u0dc0\u0dbd \u0d85\u0db1\u0dd4\u0db4\u0dd6\u0dbb\u0d9a \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dd2 \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dda.<\/p>\n\n\n\n

                                             P(A\/B’) = \\frac{P(A\\cap B')}{P(B')}<\/span><\/p>\n\n\n\n

                                             =\\frac{P(A)-P(A\\cap B)}{1-P(B)}<\/span><\/p>\n\n\n\n

                                             = \\frac{\\displaystyle\\frac{\\displaystyle1}{\\displaystyle3}-\\frac{\\displaystyle1}{\\displaystyle6}}{1-\\frac14}<\/span><\/p>\n\n\n\n

                                             = \\frac{\\displaystyle1}{\\displaystyle6}\\times\\frac{\\displaystyle4}{\\displaystyle3}<\/span><\/p>\n\n\n\n

                                       P(A\/B’) = \\frac29<\/span><\/p>\n\n\n\n

                                      P(A B) = P(A) + P(B) – P(A \u2229 B)<\/p>\n\n\n\n

                                                            = \\frac13<\/span> + \\frac14<\/span> – \\frac16<\/span><\/p>\n\n\n\n

                                                    = \\frac{\\displaystyle4+3-2}{\\displaystyle12}<\/span><\/p>\n\n\n\n

                                                    = \\frac{\\displaystyle5}{\\displaystyle12}<\/span><\/p>\n\n\n\n

                                     P(A’\u2229 B’) = P(A \u222a B)’<\/p>\n\n\n\n

                                                            = 1 – P(A \u222a B)<\/p>\n\n\n\n

                                                            = 1 – \\frac{\\displaystyle5}{\\displaystyle12}<\/span><\/p>\n\n\n\n

                                     P(A’\u2229 B’) = \\frac{\\displaystyle7}{\\displaystyle12}<\/span><\/p>\n\n\n\n

                                           P(B’\/A’) = \\frac{P(A'\\cap B')}{P(A')}<\/span><\/p>\n\n\n\n

                                                = \\frac{P(A'\\cap B')}{1-P(A)}<\/span><\/p>\n\n\n\n

                                                = \\frac{\\frac{\\textstyle7}{\\textstyle12}}{\\frac{\\textstyle2}{\\textstyle3}}<\/span><\/p>\n\n\n\n

                                                P(B’\/A’) = \\frac78<\/span><\/p>\n\n\n\n

      \u201cThere is no branch of mathematics, however abstract,which may not some day be applied to phenomena of the real world.\u201d<\/span><\/strong><\/em>
      -Nikolai Ivanovich Lobachevsky-<\/span><\/p>\r\n

      \n\n\n\n

      \n
      \u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n
      <\/div>\n\n\n\n

      \u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0dba\u0dda\u0daf\u0dd3 \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0d87\u0dad\u0dd4\u0dbd\u0dad\u0dca \u0dc0\u0db1\u0dca\u0db1\u0dda \u0db8\u0dd9\u0dad\u0db1\u0da7\u0dba\u0dd2.<\/p>\n\n\n\n

      \n
      \u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n
      <\/div>\n\n\n\n

      <\/p>\n","protected":false},"excerpt":{"rendered":"

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