Probability question

Question

A die is thrown 5 times. What is the probability of obtaining a 4 or 5?

A. Zero

B. Once

C. Twice

Hint: Calculate the p(4 or 5) for a single throw

Answer 1

The probability of getting a 4 or a 5 is 2/6 = 1/3. The probability of NOT getting a 4 or a 5 is 1 - 1/3 = 2/3

Each throw is an independent event. So the probability of an event occur in multiple throws is the product of the probability of the event occurring in individual throws.

A. To get it zero times in 5 throws, we need to not get a 4 or a 5 5 times.

The probability of that happening 5 times, is the product of not getting a 4 or 5 each time, i.e., 2/3 * 2/3 * 2/3 * 2/3 * 2/3 = 32/ 243

B. To get it one time in 5 throws, we need to get a 4 or a 5 one time and not get a 4 or a 5 4 times.

That probability is 1/3 * 2/3 * 2/3 * 2/3 * 2/3 = 16 / 243

C. To get it two times in 5 throws, we need to get a 4 or a 5 two times and not get a 4 or a 5 3 times.

That probability is 1/3 * 1/3 * 2/3 * 2/3 * 2/3 = 8/243