Question

A fair six-sided die is rolled twice. What is the probability of getting a 4 on the first roll and an odd number on the second roll?

a) 1/12
b) 1/6
c) 1/9
d) 1/3

Answer 1

The probability of rolling a 4 on the first roll and an odd number on the second roll of a six-sided die is found by multiplying the individual probabilities: (1/6 for a 4) * (3/6 for an odd number) = 3/36 or 1/12. Hence, the answer is (a) 1/12.

Step-by-step explanation:

The question is asking for the probability of getting a 4 on the first roll and an odd number on the second roll of a fair six-sided die. To find this probability, first, we consider the sample space for rolling a six-sided die twice; there are 36 possible outcomes because each roll of the die has 6 outcomes, and 6 multiplied by 6 is 36 (6 x 6 = 36).

Now, to determine the probability of our specific event, we need to find the number of outcomes that satisfy our conditions. The probability of rolling a 4 on the first roll is 1/6, since there is one favorable outcome out of 6 possible outcomes. For the second roll, the event of rolling an odd number (1, 3, 5) has 3 favorable outcomes out of 6 possible outcomes.

Since the two rolls are independent events, we multiply their probabilities to get the combined probability. Therefore, the probability of a 4 on the first roll and an odd number on the second roll is (1/6) * (3/6) = 3/36 = 1/12. Thus, the correct answer is a) 1/12.