Probability 2 Question 15
15. $A$ and $B$ are two candidates seeking admission in IIT. The probability that $A$ is selected is 0.5 and the probability that both $A$ and $B$ are selected is atmost 0.3 . Is it possible that the probability of $B$ getting selected is $0.9 ?$
(1982, 2M)
Pragraph Based Questions
There are five students $S _1, S _2, S _3, S _4$ and $S _5$ in a music class and for them there are five seats $R _1, R _2, R _3, R _4$ and $R _5$ arranged in a row, where initially the seat $R _i$ is allotted to the student $S _i, i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted the five seats.
(There are two questions based on Paragraph, the question given below is one of them)
(2018 Adv.)
Show Answer
Answer:
Correct Answer: 15. (c)
Solution:
- Given, $P(A)=0.5$ and $P(A \cap B) \leq 0.3$
$$ \begin{array}{lc} \Rightarrow & P(A)+P(B)-P(A \cup B) \leq 0.3 \\ \Rightarrow & P(B) \leq 0.3+P(A \cup B)-P(A) \leq P(A \cup B)-0.2 \\ \therefore & {[\text { since, } P(A \cup B) \leq 1 \Rightarrow P(A \cup B)-0.2 \leq 0.8]} \\ \Rightarrow & P(B) \leq 0.8 \\ & P(B) \text { cannot be } 0.9 . \end{array} $$
