Question

A fair die is rolled four times. A four is considered success while all other outcomes are failures. Find the probability of 0 successes.

a) (1/16)
b) (3/16)
c) (9/16)
d) (15/16)

Answer 1

The probability of rolling a fair six-sided die four times and getting zero fours is calculated by raising the probability of not rolling a four (5/6) to the fourth power, which gives us about 9/16 or (c) as the correct answer.

Step-by-step explanation:

The question asks us to find the probability of rolling a fair six-sided die four times and getting zero successes, where a success is defined as rolling a four. The probability of rolling any specific number on a fair die is 1/6, and the probability of rolling a number that is not a four (a failure) is therefore 5/6.

To calculate the probability of no successes (no fours) in four rolls, we have to consider the probability of a failure in each roll and then multiply these probabilities because each roll is an independent event. Mathematically, this is represented by (5/6) × (5/6) × (5/6) × (5/6), which equals (5/6)^4.

Computing this, we get:
(5/6)^4 = (625/1296) ≈ 0.4823, which can be rounded to four decimal places as per the instructions given.

Therefore, the correct answer is (c) 9/16, since 625/1296 is roughly equal to 9/16 when simplified.