This Friday, Patty has a French vocabulary test as well as a Spanish vocabulary test. To prepare, she made a study card for each word, 42% of which are French. Every time she picks a card, she sticks it back in the deck and shuffles again. If Patty picks a study card from the deck 5 times during her first study session, what is the probability that exactly 4 cards have a French word? 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 = 5, k = 4, and p = 0.42.Calculate C(5, 4): Calculate C(5, 4) using the formula C(n, k) = n! / (k!(n - k)!). C(5, 4) = 5! / (4!(5 - 4)!) = 5.Calculate (0.42)^4: Calculate (0.42)^4. (0.42)^4 = 0.42 * 0.42 * 0.42 * 0.42 = 0.03093568.Calculate (1 - 0.42)^(5 - 4): Calculate (1 - 0.42)^(5 - 4). (1 - 0.42)^(5 - 4) = (0.58)^1 = 0.58.Multiply values to find probability: Multiply all the values together to find the probability. P(X = 4) = 5 * 0.03093568 * 0.58 = 0.089718976.

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This Friday, Patty has a French vocabulary test as well as a Spanish vocabulary test. To prepare, she made a study card for each word, $42\%$ of which are French. Every time she picks a card, she sticks it back in the deck and shuffles again. $\newline$ If Patty picks a study card from the deck $5$ times during her first study session, what is the probability that exactly $4$ cards have a French word? $\newline$ Write your answer as a decimal rounded to the nearest thousandth. $\newline$ ____ $\newline$

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Algebra 2

Find probabilities using the binomial distribution

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Q. This Friday, Patty has a French vocabulary test as well as a Spanish vocabulary test. To prepare, she made a study card for each word,

42\%

of which are French. Every time she picks a card, she sticks it back in the deck and shuffles again.

\newline

If Patty picks a study card from the deck

5

times during her first study session, what is the probability that exactly

4

cards have a French word?

\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, $n = 5$ , $k = 4$ , and $p = 0.42$ .
Calculate $C(5, 4)$ : Calculate $C(5, 4)$ using the formula $C(n, k) = \frac{n!}{k!(n - k)!}$ . $C(5, 4) = \frac{5!}{4!(5 - 4)!} = 5$ .
Calculate $(0.42)^4$ : Calculate $(0.42)^4$ . $(0.42)^4 = 0.42 \times 0.42 \times 0.42 \times 0.42 = 0.03093568$ .
Calculate $(1 - 0.42)^{(5 - 4)}$ : Calculate $(1 - 0.42)^{(5 - 4)}$ . $(1 - 0.42)^{(5 - 4)} = (0.58)^1 = 0.58$ .
Multiply values to find probability: Multiply all the values together to find the probability. $P(X = 4) = 5 \times 0.03093568 \times 0.58 = 0.089718976$ .