Bowling: Sarah and Thomas are going bowling. The probability that Sarah scores more than 175 is 0.4, and the probability that Thomas scores more than 175 is 0.2. Their scores are independent.

a. Find the probability that both score more than 175.

b. Given that Thomas scores more than 175, the probability that Sarah scores higher than Thomas is 0.3. Find the probability that Thomas scores more than 175 and Sarah scores higher than Thomas.

The probability that both Sarah and Thomas score more than 175 is 0.08. If we consider the condition that Thomas already scored more than 175, the probability that Sarah scores higher than Thomas is 0.06.

Explanation:

The subject matter in question involves probability calculations in mathematics. In this case, we are working with the probability of independent events which can be calculated by multiplying the individual probabilities together.

a. Find the probability that both score more than 175.

Since Sarah and Thomas's scores are independent, we can calculate the probability of both events occurring (both scoring >175) by multiplying their individual probabilities together. This gives us 0.4 × 0.2 = 0.08.

b. Given that Thomas scores more than 175, the probability that Sarah scores higher than Thomas is 0.3. Find the probability that Thomas scores more than 175 and Sarah scores higher than Thomas.

If we already know that Thomas scores more than 175 (probability of 0.2), and the probability that Sarah scores higher than Thomas given this condition is 0.3. Then, the joint probability of these two events is found by multiplying these two probabilities, which results in 0.2 × 0.3 = 0.06.

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