Question

Nuri joins a game for a car. The rule is that Nuri picks one key from the 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

Answer:0.277

Step-by-step explanation:

Given there are three boxes i.e. A , B and C

Probability of selecting any box is $P_1=\frac{1}{3}$

Box A contains 2 keys out of which is 1 is correct so Probability of selecting the right key is $P_2=\frac{1}{2}$

Box B contains 3 keys out of which is 1 is correct so Probability of selecting the right key is $P_3=\frac{1}{3}$

Box C contains 2 keys out of which is 1 is correct but we cannot use it so Probability of selecting the right key is $P_4=0$

Probability of selecting the right key is $P=P_1\times P_2+P_1\times P_2+P_1\times P_3$

$P=\frac{1}{3}\times \frac{1}{2}+\frac{1}{3}\times \frac{1}{3}+\frac{1}{3}\times 0$

$P=\frac{5}{18}$

$P=0.277$