Probabilities of occurrence of two events are respectively 0.21 and 0.49 . probability that both occ

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14.Probability

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The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occurs simultaneously is $0.16$. Then the probability that none of the two occurs is

A

$0.3$

B

$0.46$

C

$0.14$

D

None of these

Solution

(b) $P(A \cup B) = P(A) + P(B) – P(A \cap B)$

$ = 0.21 + 0.49 – 0.16 \Rightarrow P(A \cup B) = 0.54$

Probability of none of two occurs

$ = 1 – P(A \cup B) = 1 – 0.54 = 0.46.$

Standard 11

Mathematics

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