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.

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RenatoMattice RenatoMattice · Answer 1 · 2019-02-19T07:22:11+01:00

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%

Step-by-step explanation:

Since we have given that

Probability of heavy fog is given by

[tex]P(F)=0.70[/tex]

Probability of a light drizzle is given by

[tex]P(D)=0.30[/tex]

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

[tex]P(C\mid D)=0.80[/tex]

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

[tex]P(C\mid F)=0.30[/tex]

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

Probability of getting the game be cancelled is given by

[tex]P(C)=P(F)\times P(C\mid F)+P(D)\times P(C\mid D)\\\\P(C)=0.70\times 0.30+0.30\times 0.80\\\\P(C)=0.45\\\\P(C)=45\%[/tex]

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

[tex]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\%[/tex]

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%