Question

An insurer is studying the characteristics of those who buy its policies. It discovered​ that, among young​ drivers, 30​% insure a​ foreign-made car. Among those who drive​ foreign-made cars, the insurer also discovered that 30​% are young. Consider the events Y = ​{randomly chosen driver is​ young} and F = ​{randomly chosen driver insures​ foreign-made car}. Does the insurer cover more drivers who are young or more drivers who insure​ foreign-made cars?

Can you also include an explanation? Thanks!

Answer 1

Y = ​{randomly chosen driver is​ young}

F = ​{randomly chosen driver insures​ foreign-made car}.

among young​ drivers, 30​% insure a​ foreign-made car

This is conditional probability where we know that the driver is young.

P(F | Y) = 0.3

Among those who drive​ foreign-made cars, the insurer also discovered that 30​% are young.

This is conditional probability where we know that the driver has a foreign car

P(Y|F) = 0.3

The conditional probabiltiy formula is

Therefore using this we have

P(F | Y) = 0.3

...........(1)

P(Y|F) = 0.3

.........(2)

Equating eq (1) and (2)

0.3P(Y) = 0.3P(F)

Therefore

P(Y) = P(F)

This shows that the insurer cover same drivers who are young as well drivers who insure​ foreign-made cars.