Probability w/Tree Diagrams - Midterm Review

A pitcher on Ashton's little league baseball team can throw 2 types of pitches: a fastball and a knuckleball.

70% of his pitches are fastballs.

60% of his fastballs are strikes.

20% of his knuckleballs are strikes.

Complete the tree diagram by labeling the branches with the correct probabilities.

a

b

c

d

e

f

0.5

0.9

0.6

0.3

1

0.4

0.1

0.8

0.2

0.7

Answer explanation

Remember, each set of branches must add to 1.

Whenever Sean has a quiz tomorrow, there is an 80% chance that he will review the night before.

Past results have shown that when Sean reviews, he passes 90% of the time. If he doesn't review, then he only passes 25% of the time.

Sean had a quiz yesterday.

What is the probability he reviewed and passed?

Mathematical Equivalence

ON

Answer explanation

Remember: to find the probability of one outcome at the end of a tree diagram, you MULTIPLY all the probabilities along the path to that outcome.

Whenever Sean has a quiz tomorrow, there is an 80% chance that he will review the night before.

Past results have shown that when Sean reviews, he passes 90% of the time. If he doesn't review, then he only passes 25% of the time.

Sean had a quiz yesterday.

What is the probability he passed but didn't review?

Mathematical Equivalence

ON

Answer explanation

Remember: to find the probability of one outcome at the end of a tree diagram, you MULTIPLY all the probabilities along the path to that outcome.

Whenever Sean has a quiz tomorrow, there is an 80% chance that he will review the night before.

Past results have shown that when Sean reviews, he passes 90% of the time. If he doesn't review, then he only passes 25% of the time.

Sean had a quiz yesterday.

What is the probability he failed the quiz?

Mathematical Equivalence

ON

Answer explanation

Remember: the outcomes at the end of the tree are all mutually exclusive. So, the simple addition rule for probability applies.

P(A or B) = P(A) + P(B)

At Bob’s Burger Shop, you can order a burger with your choice of fries or salad and a soda or juice. The diagram below show the orders taken of one day.

Of the order with fries, what is the probability that they would have juice?

• 75/500 = 3/20

• 25/500 = 1/20

• 25/150 = 1/6

• 75/350 = 3/14

At Bob’s Burger Shop, you can order a burger with your choice of fries or salad and a soda or juice. The diagram below show the orders taken of one day.

Of the order with a salad, what is the probability that they would have juice?

• 75/500 = 3/20

• 25/500 = 1/20

• 25/150 = 1/6

• 75/350 = 3/14

At Bob’s Burger Shop, you can order a burger with your choice of fries or salad and a soda or juice. The diagram below show the orders taken of one day.

What is the probability of ordering fries?

• 350/500 = 70%

• 500/350 = 142%

• 350/150 = 233%

• 75/350 = 21%

At Bob’s Burger Shop, you can order a burger with your choice of fries or salad and a soda or juice. The diagram below show the orders taken of one day.

What is the probability of ordering fries and a coke?

• 275/500 = 55%

• 75/500 = 15%

• 275/350 = 79%

• 625/350 = 179%

At Bob’s Burger Shop, you can order a burger with your choice of fries or salad and a soda or juice. The diagram below show the orders taken of one day.

Of the order with fries, what is the probability they would have a coke?

• 625/500 = 125%

• 75/500 = 15%

• 275/350 = 79%

• 625/350 = 179%

At Bob’s Burger Shop, you can order a burger with your choice of fries or salad and a soda or juice. The diagram below show the orders taken of one day.

What is the probability of ordering a salad?

• 125/500 = 1/4

• 25/500 = 1/20

• 500/150 = 10/3

• 150/500 = 3/10