A basket contains 11 fruits, 4 are apples and 7 are bananas. Two fruits are drawn without replacement. What is the probability that the first fruit is an apple and the second fruit is a banana?
Options
A
B
C
D
Answer & Analysis
Answer
B
Analysis
Question Analysis
This question focuses on testing the basic application of the multiplication rule for dependent events.
The key lies in correctly calculating the probability of each draw while taking into account the change in the sample space after the first draw.
Key Concept Explanation
Dependent events mean that the outcome of the first fruit draw influences the probability of the second draw.
The multiplication rule for dependent events, , is used here.
Step-by-Step Solution
Calculate the probability of drawing an apple on the first draw:
There are 4 apples out of 11 total fruits, so .
Calculate the probability of drawing a banana on the second draw given that an apple was drawn on the first draw:
After removing one apple, there are 10 fruits left, and 7 of them are bananas. So
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