Question

In a certain country, the probability that a woman reaches the age of 70 is 0.7

and the probability that a woman lives to be 80 is 0.5.

(a) If a woman from that country is 70 years old, what is the conditional probability that

she will survive to 80 years?

(b) Suppose that three sisters born in that country live completely independent lives. What

is the probability that they will all be alive at the age of 70?

(c) If the three sisters are all alive at the age of 70, what is the probability that they will

all be alive at the age of 80?

Question 9: A slot machine at a ca

Answer 1

(a)

Let

A = Event of living up to 70 years

B = Event of living up to 80 years

Given:
P(A) = 0.7

P(B) = 0.5

By Multiplication Theorem of Probability:

P(B/A) = P(AB)/P(A)

Using Multiplication Theorem of Probability:,

the conditional probability that she will survive to 80 years= P(A/B) = 0.5/0.7 = 0.7143

So,

Answer is:

0.7143

(b)

the probability that they will all be alive at the age of 70 = 0.7³ = 0.343

So,

Answer is:

0.343

(c)

If the three sisters are all alive at the age of 70, the probability that they will all be alive at the age of 80 = 0.7143³ =0.3645

So,

Answer is:

0.3645