Answer :
Final answer:
The probabilities stated in statements a) and b) are correct, while the probabilities in statements c) and d) are incorrect.
Explanation:
Let's analyze each statement to determine if it is true or false:
a) The probability that both Sarah and Thomas score more than 175 is 0.08: To determine the probability of two independent events occurring together, we multiply their individual probabilities. Therefore, if the probability of Sarah scoring more than 175 is 0.4 and the probability of Thomas scoring more than 175 is 0.2, the probability of both Sarah and Thomas scoring more than 175 is 0.4 x 0.2 = 0.08. This statement is true.
b) The probability that either Sarah or Thomas score more than 175 is 0.6: The probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. Therefore, if the probability of Sarah scoring more than 175 is 0.4 and the probability of Thomas scoring more than 175 is 0.2, the probability of either Sarah or Thomas scoring more than 175 is 0.4 + 0.2 = 0.6. This statement is true.
c) The probability that neither Sarah nor Thomas score more than 175 is 0.48: The probability of an event not occurring is equal to 1 minus the probability of the event occurring. Therefore, if the probability of either Sarah or Thomas scoring more than 175 is 0.6, the probability of neither of them scoring more than 175 is 1 - 0.6 = 0.4. However, this statement states that the probability is 0.48, which is incorrect. This statement is false.
d) The probability that at least one of them scores more than 175 is 0.6: The probability of at least one of two events occurring is equal to 1 minus the probability of neither event occurring. Therefore, if the probability of neither Sarah nor Thomas scoring more than 175 is 0.4, the probability of at least one of them scoring more than 175 is 1 - 0.4 = 0.6. This statement is true.
