Question

What is the probability of getting a 4 each time if a die is rolled 3 times?

a. 1/216


b. 1/120


c. 1/1296


d. 3/6

Answer 1

a. 1/216

Explanation:

To solve this problem let's call h the probability of getting a 4 when throwing a die.

Each throw of the die is an independent event, since the result obtained by throwing the dice the first time, does not condition the result obtained by throwing the die a second time.

The probability of h is:

P(h) = 1/6 (because the die has six faces)

We want to know the probability of getting a 4 three consecutive times. Since the events are independent, then this is:

P (h and h and h) = P (h)*P(h)*P (h)

P (h and h and h) = (1/6) ^ 3

P (h and h and h) = (1/6) ^ 3

P (h and h and h) = 1/216

Answer 2

The correct answer option is b. 1/216.

Explanation:

The probability of getting a 4 when a die is rolled is
`(1)/(6)` which can be written as:

P (4) =
`(1)/(6)`

So to find the probability of getting a 4 each time if a die is rolled 3 times, we will multiply the probability of getting a 4 by 3.

P (getting a 4 each time when die is rolled 3 times) =
`(1)/(6) * 3` = 1/216