Answer to Question #178584 in Statistics and Probability for Atubiga

Question

The probability that Melcom Company will survive for the next 10 years is 0.75 the probability that Life Company will survive for the next 10 years is 0.80. What is the probability that:

(i) both will survive for the next 10 years

(ii) neither will survive for the next 10 years

Answer 1

The probability that Melcom Company will survive for the next 10 years P(A)= 0.75

and the probability that Life Company will survive for the next 10 years P(B)=0.80

(i) The probability that both will survive for the next 10 years

$P(A\ UB)=P(A)+P(B)-P(A\cap B)$

$P(A\cap B)=P(A)+P(B)-P(A\ UB)$

$P(A\cap B)=0.75+0.80-1\\P(A\cap B)=0.55$

(ii) The probability neither will survive for the next 10 years = $1-P(A\cap B)$

=$1-0.55=0.45$