Todd bought new equipment for his bowling alley, including a ball return machine. There is a 66% chance that the machine returns a bowling ball with the finger holes facing up. If the machine returns 3 bowling balls, what is the probability that exactly 2 will have the finger holes facing up? Write your answer as a decimal rounded to the nearest thousandth. ____

Use Binomial Probability Formula: Use the binomial probability formula: P(X = k) = C(n, k) * (p)^k * (1-p)^(n-k). Here, n = 3, k = 2, and p = 0.66.Calculate Combination: Calculate C(3, 2) using the formula C(n, k) = n! / k! (n - k)!. So, C(3, 2) = 3! / 2! (3 - 2)! = 3.Calculate Success Probability: Solve (0.66)^2 to get the probability of success twice. (0.66)^2 = 0.4356.Calculate Failure Probability: Calculate (1 - 0.66)^(3 - 2) for the probability of one failure. (1 - 0.66)^(3 - 2) = 0.34.Multiply Values: Multiply all the values together: P(X = 2) = 3 * 0.4356 * 0.34. P(X = 2) = 0.444264.Round to Nearest Thousandth: Round the answer to the nearest thousandth: P(X = 2) = 0.444.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Todd bought new equipment for his bowling alley, including a ball return machine. There is a $66\%$ chance that the machine returns a bowling ball with the finger holes facing up. $\newline$ If the machine returns $3$ bowling balls, what is the probability that exactly $2$ will have the finger holes facing up? $\newline$ Write your answer as a decimal rounded to the nearest thousandth. $\newline$ ____ $\newline$

View step-by-step help

Home

Math Problems

Algebra 2

Find probabilities using the binomial distribution

Full solution

Q. Todd bought new equipment for his bowling alley, including a ball return machine. There is a

66\%

chance that the machine returns a bowling ball with the finger holes facing up.

\newline

If the machine returns

3

bowling balls, what is the probability that exactly

2

will have the finger holes facing up?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

____

\newline

Use Binomial Probability Formula: Use the binomial probability formula: $P(X = k) = C(n, k) \cdot (p)^k \cdot (1-p)^{(n-k)}$ . Here, $n = 3$ , $k = 2$ , and $p = 0.66$ .
Calculate Combination: Calculate $C(3, 2)$ using the formula $C(n, k) = \frac{n!}{k!(n - k)!}$ . So, $C(3, 2) = \frac{3!}{2!(3 - 2)!} = 3$ .
Calculate Success Probability: Solve $(0.66)^2$ to get the probability of success twice. $(0.66)^2 = 0.4356$ .
Calculate Failure Probability: Calculate $(1 - 0.66)^{(3 - 2)}$ for the probability of one failure. $(1 - 0.66)^{(3 - 2)} = 0.34$ .
Multiply Values: Multiply all the values together: $P(X = 2) = 3 \times 0.4356 \times 0.34$ . $P(X = 2) = 0.444264$ .
Round to Nearest Thousandth: Round the answer to the nearest thousandth: $P(X = 2) = 0.444$ .