Question

# A test has three multiple choice questions that offer five possible answers. Draw a tree diagram that shows all the possible multiple-choice combinations for the answers to the test and determine the probability that a student will get two out of three questions correct by guessing on all of them.

A
12125
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B
16125
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C
12145
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D
16145
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Solution

## The correct option is A 12125Given that there are 3 questions and each question has 5 possible answers.The number of possible multiple choice combinations are 5×5×5=125In each question , the probability of guessing correct is 15 and probability of guessing wrong is 45.Out of 3 questions , the probability of getting two questions correct is 3C2×(15)2×45=12125

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