Question

We roll a fair die four times. Let A be the event that there are at least two fives among the four rolls. What is the probability of event A?

1) 1/1296
2) 1/216
3) 1/36
4) 5/6

Answer 1

To find the probability of event A, which is the event of getting at least two fives in four rolls of a fair die, we can use the concept of combinations.

Step-by-step explanation:

To find the probability of event A, which is the event of getting at least two fives in four rolls of a fair die, we can use the concept of combinations.

The probability of getting exactly two fives is given by:

P(2 fives) = C(4, 2) * (1/6)^2 * (5/6)^2

The probability of getting exactly three fives is given by:

P(3 fives) = C(4, 3) * (1/6)^3 * (5/6)^1

The probability of getting exactly four fives is given by:

P(4 fives) = C(4, 4) * (1/6)^4 * (5/6)^0

The total probability of event A is the sum of these probabilities:

P(A) = P(2 fives) + P(3 fives) + P(4 fives)

Calculating these probabilities, we find that the probability of event A is 11/1296.