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Assume the random variable $X$ has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and
the probability of obtaining a success.
$P(X = 4)$, $n = 15$, $p = 0.5$
You can also solve this using technology.
For this problem, we know that $x = 4$, $n = 15$, and $p = 0.5$. We can start by substituting these values into the formula for the binomial distribution. Simplify each part
of the expression below, rounding your answers to six decimal places, if necessary.
$P(X = x) = \binom{n}{x} \cdot p^x \cdot (1 - p)^{(n - x)}$
$P(X = 4) = \binom{15}{4} \cdot (0.5)^4 \cdot (1 - 0.5)^{(15 - 4)}$
$\approx \frac{15!}{4!11!} (0.5)^4 (0.5)^{11}$
$\approx (2.17492) (0.0625) (0.00049)$
Correct Answer: $P(X = 4) \approx (1365)(0.0625)(0.000488)$
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3:51 PM
1/5/2022