(A) Let $A$ and $B$ be the events of passing the first and second examinations,respectively.Given: $P(A) = 0.8$,$P(B) = 0.7$,and $P(A \cup B) = 0.95$.

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(A) Let $A$ and $B$ be the events of passing the first and second examinations,respectively.Given: $P(A) = 0.8$,$P(B) = 0.7$,and $P(A \cup B) = 0.95$.We know the addition theorem of probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the given values: $0.95 = 0.8 + 0.7 - P(A \cap B)$.$0.95 = 1.5 - P(A \cap B)$.$P(A \cap B) = 1.5 - 0.95 = 0.55$.Thus,the probability of passing both examinations is $0.55$.

Class 11 Mathematics Probability Odds in favor and odds against, Addition theorem on probability

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In an entrance test that is graded on the basis of two examinations,the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7$. The probability of passing at least one of them is $0.95$. What is the probability of passing both?

A
$0.55$
B
$0.45$
C
$0.35$
D
$0.65$

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Class 11

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Probability

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Odds in favor and odds against, Addition theorem on probability

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Medium

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