Question

Make a tree diagram and find each probability.

A softball game has an 80% chance of being canceled for a light drizzle and a 30% chance of being canceled for a heavy fog when there is no drizzle. There is a 70% chance of heavy fog and a 30% chance of a light drizzle.

a. Find the probability that the game will be canceled.
b. Find the probability there will be a light drizzle and the game will not be canceled.

Be sure to show all work.

Answer 1

Answer: a) probability that the game will be canceled= 45%

b) probability there will be a light drizzle and the game will not be canceled=20%

Explanation:

Since we have given that

Probability of heavy fog is given by

`P(F)=0.70`

Probability of a light drizzle is given by

`P(D)=0.30`

Probability of getting canceled a softball game due to light drizzle is given by

`P(C\mid D)=0.80`

Probability of getting canceled a softball game due to heavy fog is given by

`P(C\mid F)=0.30`

a. Find the probability that the game will be canceled.

Probability of getting the game be cancelled is given by

`P(C)=P(F)* P(C\mid F)+P(D)* P(C\mid D)\\\\P(C)=0.70* 0.30+0.30* 0.80\\\\P(C)=0.45\\\\P(C)=45\%`

b. Find the probability there will be a light drizzle and the game will not be canceled.

Probability that there will be a light drizzle and the game will not be canceled is given by

`P(C'\mid D)=1-P(C\mid D)\\\\P(C'\mid D)=1-0.80\\\\P(C'\mid D)=0.20\\\\P(C'\mid D)=20\%`

Hence, a) probability that the game will be canceled= 45%

b) probability there will be a light drizzle and the game will not be canceled=20%