Probability that a student will succeed in II | vedclass

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Question

(d) Let $A$ denotes the event that the student is selected in $IIT$ entrance test and $B$ denotes the event that he is selected in Roorkee entrance te

Vedclass · Accepted Answer

$0.6$

Vedclass · Answer

(d) Let $A$ denotes the event that the student is selected in $IIT$ entrance test and $B$ denotes the event that he is selected in Roorkee entrance test. Then

$P(A) = 0.2,\,\,P(B) = 0.5$ and $P(A \cap B) = 0.3.$

Required probability $ = P(\overline A \cap \overline  B) = 1 - P(A \cup B)$

$ = 1 - (P(A) + P(B) - P(A \cap B))$

$ = 1 - (0.2 + 0.5 - 0.3) = 0.6$.

Probability that a student will succeed in $IIT$ entrance test is $0.2$ and that he will succeed in Roorkee entrance test is $0.5$. If the probability that he will be successful at both the places is $0.3$, then the probability that he does not succeed at both the places is

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