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14.Probability
medium
An experiment has $10$ equally likely outcomes. Let $\mathrm{A}$ and $\mathrm{B}$ be two non-empty events of the experiment. If $\mathrm{A}$ consists of $4$ outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent, is
A
$2,4$ or $8$
B
$3,6$ or $9$
C
$4$ or $8$
D
$5$ or $10$
(IIT-2008)
Solution
$ \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{4}{10} \times \frac{\mathrm{p}}{10}=\frac{2 \mathrm{p} / 5}{10} $
$ \Rightarrow \frac{2 \mathrm{p}}{5} \text { is an integer } $
$ \Rightarrow \mathrm{p}=5 \text { or } 10 .$
Standard 11
Mathematics
Similar Questions
Fill in the blanks in following table :
| $P(A)$ | $P(B)$ | $P(A \cap B)$ | $P (A \cup B)$ |
| $0.35$ | ……….. | $0.25$ | $0.6$ |
easy
