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The probabilities that a man and his wife live ... - JAMB Mathematics 2012 Question

The probabilities that a man and his wife live for 80 years are 23 and 35 respectively. Find the probability that at least one of them will live up to 80 years
A
215
B
315
C
715
D
1315
correct option: d

Man lives = (\frac{2}{3}) not live = (\frac{1}{3})

Wife lives = (\frac{3}{5}) not live = (\frac{2}{5})

(P(\frac{2}{3} \times \frac{2}{5}) + (\frac{2}{5} \times \frac{1}{3}) + (\frac{2}{3} \times \frac{3}{5}))

= (\frac{4}{15} + \frac{3}{15} + \frac{6}{15})

= (\frac{13}{15})

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