Consider a partially completed tree diagram for rolling 2 dice with the following outcomes: {1, prime number, composite number}. The probability that the first branch of the tree is a composite number is , and the probability that the second branch is also composite is , so the probability that both rolls are composite is
Question
Consider a partially completed tree diagram for rolling 2 dice with the following outcomes: {1, prime number, composite number}. The probability that the first branch of the tree is a composite number is , and the probability that the second branch is also composite is , so the probability that both rolls are composite is
Solution
It seems like you've missed out on providing the actual probabilities for the first and second branch being a composite number. However, I can explain the process to you.
When rolling a die, the possible outcomes are {1,2,3,4,5,6}. Out of these, the prime numbers are {2,3,5} and the composite numbers are {4,6}.
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The probability of rolling a composite number on a single die is the number of composite outcomes divided by the total number of outcomes. So, P(composite) = Number of composite numbers / Total outcomes = 2/6 = 1/3.
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If you're rolling the die twice and you want the probability that both rolls result in a composite number, you multiply the probabilities of each individual roll. So, P(both composite) = P(composite on first roll) * P(composite on second roll) = (1/3) * (1/3) = 1/9.
Please replace the probabilities (1/3 in this case) with the actual probabilities you have, if they are different.
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