Question

The odds against a husband who is 55 years old living till he is 75 is 8 : 5 and it is 4 : 3 against his wife who is now 48, living till she is 68. Find the probability that
a) the couple will be alive 20 years hence
b) at least one of them will be alive 20 years hence.

Answer 1

Answer:

a) 15/91

b) 59/91

Step-by-step explanation:

Hi,

Odds against a certain event =

No of unfavorable outcome/Total number of outcome

Let E be any event whose odds against the event are a : b

Number of Unfavorable Outcomes/Number of Favorable Outcomes = a/b

1 + Number of Unfavorable Outcomes/Number of Favorable Outcomes

= 1 + a/b

(Number of Favorable Outcomes  + Number of Unfavorable

Outcomes)/Number of Favorable Outcomes = (a + b)/b

Total number of outcomes/Number of favorable outcomes = (a + b)/b

P(E) = Number of Favorable Outcomes/Total number of outcomes

= b/(a + b)

Let 'H' be the event that husband whose is age is 55 lives till 75 and

odds against it are 8 : 5

So, P(H) = 5/(8 + 5) = 5/13

Let 'W' be the event that wife whose is age is 48 lives till 68 and odds

against it are 4 : 3

So, P(W) = 3/(3 + 4) = 3/7

a) Probability that couple will live 20 years hence

= P(H ∩ W)

But H and W are independent events, so

P(H ∩ W) = P(H)P(W) = 3/7*5/13

= 15/91

a)Chance that at least one of Husband or Wife will be alive is

= P(H ∪ W) = P(H) + P(W) - P(H ∩ W)

= 5/13 + 3/7 - 15/91

= 59/91

Hope, it helps !