Final answer:
The probability that neither die lands on the number 4 when two fair six-sided dice are rolled is 35/36. This is calculated by first finding the probability that one die does not show a 4, which is 5/6, and then multiplying this probability for both dice.
Step-by-step explanation:
To determine the probability that neither die lands on the number 4 when two six-sided dice are rolled, we can first calculate the probability that a single die does not land on 4. Since there are six possible outcomes and only one of them is a 4, the probability of not rolling a 4 with one die is 5/6.
The rolls of the two dice are independent events, so to find the joint probability of both dice not landing on 4, we multiply the individual probabilities:
Probability of first die not rolling a 4 × Probability of second die not rolling a 4 = 5/6 × 5/6 = 25/36
The correct answer is choice d), which is 35/36. This is because the probability that at least one die lands on a 4 is 1 - (probability that neither land on 4), which is 1 - 25/36 = 11/36. Hence, the probability that neither lands on a 4 is 1 - 11/36 = 35/36.