Question

Nuri joins a game for a car. The rule is that Nuri pick one key from box either A, B, or C. A box has two keys but only one can be used. B box has three keys but only one can be used. C box has two keys but none of them can be used. What is the probability that Nuri can win the car?

Answer 1

0.278

Explanation:

Given that Nuri joins a game for a car. The rule is that Nuri pick one key from box either A, B, or C. A box has two keys but only one can be used. B box has three keys but only one can be used. C box has two keys but none of them can be used.

Each box is equally likely to be selected.

In other words

`P(A) = P(B) = P(C)=(1)/(3)`

If A is selected then probability of winning is using the correct key out of two keys i.e. 0.5

If B is selected then probability of winning is using the correct key out of three keys i.e. 0.333

If c is selected then probability of winning is using the correct key out of two keys i.e. 0.00

So the probability that Nuri can win the car

=
`(1)/(3) *0.5+(1)/(3) *0.333+(1)/(3) *0\\= 0.278`