Question

What is the probability of getting a number less than three on a fair die and a tail on a coin flip>

1/12
1/6
1/4
1/2

My answer was 1/2 due to 3/6 and simplifying it.

Answer 1

I would say 1/6 because you would get 2/6 of a chance of rolling a number under 3 on a fair die and 1/2 of a chance of getting a tail on a coin flip. Once you multiply those two together and simplify it, you would get 1/6.

Answer 2

1/6

Explanation:

Let's call

• Event A: A dice is rolled and a number lower than 3 is obtained.

• Event B: A coin is flipped and it shows tail.

For Event A, you could get 6 possible results (1, 2, 3, 4, 5, 6). But, only 2 (1, 2) are lower than 3. Then, P(A) = 2/6 = 1/3.

For Event B, you could get 2 possible results (head, tail) and only 1 (tail) fulfills the condition. Then, P(B) = 1/2.

A and B are independent events and the probability that both occur is equal to the product of the individual probabilities.

P(A ∩ B) = P(A) . P(B) = 1/3 . 1/2 = 1/6