Question15. Mrs. Echols chooses a student at random from the Coronado High School student body, and the following events are recorded:
: the student is male
: the student is female
B : the student ate breakfast that morning
N : the student did not eat breakfast that morning
The tree diagram gives probabilities associated with these events.
Find and write in words what this expression represents.
a) 0.18 . This is the probability the student ate breakfast and is female.
b) 0.18 . This is the probability the student ate breakfast, given she is female.
c) 0.18 . This is the probability the student is female, given she ate breakfast.
d) 0.30 . This is the probability the student ate breakfast, given she is female.
e) 0.30 . This is the probability the student is female, given she ate breakfast.
Studdy Solution
STEP 1
1. The tree diagram provides the probabilities for the events involving gender and breakfast consumption.
2. We are tasked with finding , which is the probability that a student ate breakfast given that the student is female.
STEP 2
1. Identify the relevant probabilities from the tree diagram.
2. Use the conditional probability formula to find .
3. Interpret the result in words.
STEP 3
Identify the probability that a student is female, , and the probability that a female student ate breakfast, .
From the tree diagram:
STEP 4
Use the conditional probability formula:
Given , and , calculate :
STEP 5
Interpret :
The expression represents the probability that a student ate breakfast given that the student is female.
The correct choice is:
d) 0.30 . This is the probability the student ate breakfast, given she is female.
The solution is:
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