A) \[\frac{13}{15}\]
B) \[\frac{7}{15}\]
C) \[\frac{4}{15}\]
D) None of these
Correct Answer: A
Solution :
Let \[A\] be the event that the husband will be alive 20 years. \[B\] be the event that the wife will be alive 20 years. Clearly \[A\] and \[B\] are independent events \ \[P(A\cap B)=P(A).\,P(B)\] Given \[P(A)=\frac{3}{5},\] \[P(B)=\frac{2}{3}\] The probability that at least of them will be alive 20 years is \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[=P(A)+P(B)-P(A)P(B)=\frac{3}{5}+\frac{2}{3}-\frac{3}{5}.\frac{2}{3}=\frac{9+10-6}{15}=\frac{13}{15}\] Aliter : Required probability is \[1-P(A\]and \[B\] both will die) \[=1-\frac{2}{5}\times \frac{1}{3}=1-\frac{2}{15}=\frac{13}{15}.\]You need to login to perform this action.
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