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A student rolls a number cube. What is the probability the student rolled a 5, given that the student rolled a prime number?

A. 1/6
B. 1/3
C. 1/2
D. 5/6

1 Answer

2 votes

Final answer:

The probability of rolling a 5 given that the number rolled is a prime number is 1/3, since there are three prime numbers on a six-sided die {2, 3, 5} and only one of them is a 5.

Step-by-step explanation:

The question asks for the probability of rolling a 5, given that we have rolled a prime number on a six-sided die. There are three prime numbers on a six-sided die: {2, 3, 5}. Since these are the only prime numbers we could have rolled, and the event specifies that we did roll a prime, we now only consider these numbers as possible outcomes.

Now, we are interested in the probability that the number rolled is specifically a 5 among the prime numbers {2, 3, 5}. There is only one '5' in the set of prime outcomes, so the probability is 1 out of 3. Thus, the correct answer is 1/3, which corresponds to option B.

User Ryan Wright
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