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If a fair coin is tossed 4 times, what is the probability, to the nearest thousandth, of getting exactly 2 tails?
Answer:

If a fair coin is tossed $4$ times, what is the probability, to the nearest thousandth, of getting exactly $2$ tails? $\newline$ Answer:

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Full solution

Q. If a fair coin is tossed

4

times, what is the probability, to the nearest thousandth, of getting exactly

2

tails?

\newline

Answer:

Understand the problem: Understand the problem. $\newline$ We need to calculate the probability of getting exactly $2$ tails in $4$ tosses of a fair coin.
Determine total outcomes: Determine the total number of outcomes for $4$ coin tosses. $\newline$ Since each coin toss has $2$ possible outcomes (heads or tails), for $4$ tosses, the total number of outcomes is $2^4$ . $\newline$ Total outcomes = $2 \times 2 \times 2 \times 2 = 16$
Determine favorable outcomes: Determine the number of favorable outcomes for getting exactly $2$ tails. $\newline$ We can use the binomial coefficient for this, which is given by ＂ $n$ choose $k$ ＂ where $n$ is the total number of events ( $4$ coin tosses) and $k$ is the number of successful events ( $2$ tails). $\newline$ The binomial coefficient formula is $C(n, k) = \frac{n!}{k! * (n - k)!}$ . $\newline$ $C(4, 2) = \frac{4!}{2! * (4 - 2)!} = \frac{(4 * 3 * 2 * 1)}{(2 * 1 * 2 * 1)} = 6$
Calculate probability: Calculate the probability of getting exactly $2$ tails. $\newline$ The probability is the number of favorable outcomes divided by the total number of outcomes. $\newline$ Probability = Favorable outcomes / Total outcomes = $\frac{6}{16}$
Simplify and round: Simplify the probability and round to the nearest thousandth. $\newline$ Probability = $\frac{6}{16} = 0.375$ $\newline$ When rounded to the nearest thousandth, the probability is $0.375$ .

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