65% of cows on a farm are pregnant. If 2 cows are chosen at random, what is the probability that exactly 1 is pregnant? Write your answer as a decimal rounded to the nearest thousandth. ____

Calculate first cow probability: First, calculate the probability that the first cow is pregnant and the second is not. The probability of the first cow being pregnant is 65%, or 0.65. The probability of the second cow not being pregnant is 35%, or 0.35. So, the probability of this scenario is 0.65 * 0.35.Calculate second cow probability: Now, calculate the probability that the first cow is not pregnant and the second is. The probability of the first cow not being pregnant is 35%, or 0.35. The probability of the second cow being pregnant is 65%, or 0.65. So, the probability of this scenario is 0.35 * 0.65.Add probabilities: Add the two probabilities together to find the total probability that exactly one cow is pregnant. 0.65 * 0.35 + 0.35 * 0.65.Perform calculations: Perform the calculations: 0.65 * 0.35 = 0.2275 0.35 * 0.65 = 0.2275 0.2275 + 0.2275 = 0.455Round the result: Round the result to the nearest thousandth. The rounded probability is 0.455.

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$\newline$ $65\%$ of cows on a farm are pregnant. $\newline$ If $2$ cows are chosen at random, what is the probability that exactly $1$ is pregnant? $\newline$ Write your answer as a decimal rounded to the nearest thousandth. $\newline$ ____ $\newline$

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Math Problems

Precalculus

Find probabilities using the binomial distribution

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\newline

65\%

of cows on a farm are pregnant.

\newline

2

cows are chosen at random, what is the probability that exactly

1

is pregnant?

\newline

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

\newline

____

\newline

Calculate first cow probability: First, calculate the probability that the first cow is pregnant and the second is not. $\newline$ The probability of the first cow being pregnant is $65\%$ , or $0.65$ . $\newline$ The probability of the second cow not being pregnant is $35\%$ , or $0.35$ . $\newline$ So, the probability of this scenario is $0.65 \times 0.35$ .
Calculate second cow probability: Now, calculate the probability that the first cow is not pregnant and the second is. $\newline$ The probability of the first cow not being pregnant is $35$ \%, or $0.35$ . $\newline$ The probability of the second cow being pregnant is $65$ \%, or $0.65$ . $\newline$ So, the probability of this scenario is $0.35 \times 0.65$ .
Add probabilities: Add the two probabilities together to find the total probability that exactly one cow is pregnant. $0.65 \times 0.35 + 0.35 \times 0.65$ .
Perform calculations: Perform the calculations: $\newline$ $0.65 \times 0.35 = 0.2275$ $\newline$ $0.35 \times 0.65 = 0.2275$ $\newline$ $0.2275 + 0.2275 = 0.455$
Round the result: Round the result to the nearest thousandth. $\newline$ The rounded probability is $0.455$ .