When rolling two dice, the probability of rolling doubles is 1/6. Suppose that a game player rolls the dice five times, hoping to roll doubles. What is the probability the player gets doubles less than three times in 5 attempts?

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AFOKE88 AFOKE88 · Answer 1 · 2022-04-29T22:11:53+02:00

The probability that the player gets doubles less than three times in 5 attempts is; 0.9645.

The formula for binomial probability distribution is;

P(X = x) = ⁿCₓ × pˣ × (1 - p)⁽ⁿ ⁻ ˣ⁾

where;

x = total number of successes

p = probability of a success on an individual trial

n = number of trials

We are given;

x = 3

p = 1/6 = 0.1667

n = 5

Thus;

P(X < 3) = (⁵C₂ * 0.1667 * (1 - 0.1667)⁽⁵ ⁻ ²⁾) + (⁵C₁ * 0.1667 * (1 - 0.1667)⁽⁵ ⁻ ¹⁾) + (⁵C₀ * 0.1667 * (1 - 0.1667)⁽⁵ ⁻ ⁰⁾)

Thus;

P(X < 3) = 0.9645

Thus, the probability that the player gets doubles less than three times in 5 attempts is 0.9645.

Read more about Binomial Probaility at; https://brainly.com/question/15246027