- Home
- Standard 11
- Mathematics
14.Probability
hard
નિદેશાવકાશમાં કોઇ બે ઘટનાઓ $A$ અને $B$ માટે,
A
$P\,\left( {\frac{A}{B}} \right) \ge \frac{{P(A) + P(B) - 1}}{{P(B)}},\,\,P(B) \ne 0$ હંમેશા સત્ય છે.
B
$P\,(A \cap \bar B) = P(A) - P(A \cap B)$ શક્ય થાય નહિ.
C
જો $A$ અને $ B$ એ અલગ ગણ હોય, તો $P\,(A \cup B) = 1 - P(\bar A)\,P(\bar B),$
D
એકપણ નહિ.
(IIT-1991)
Solution
(a) We know that $P(A/B) = \frac{{P(A \cap B)}}{{P(B)}}$
Also we know that $P(A \cup B) \le 1$
$ \Rightarrow P(A) + P(B) – P(A \cap B) \le 1$
$ \Rightarrow P(A \cap B) \ge P(A) + P(B) – 1$
$ \Rightarrow \frac{{P(A \cap B)}}{{P(B)}} \ge \frac{{P(A) + P(B) – 1}}{{P(B)}}$
$ \Rightarrow P(A/B) \ge \frac{{P(A) + P(B) – 1}}{{P(B)}}$
Standard 11
Mathematics
