Question

pre-test complete
time remaining 54:18
aron flips a penny 9 times. which expression represents the probability of getting exactly 3 heads?
$p(k \text{ successes})=_{n}c_{k}p^{k}(1-p)^{n-k}$
$_{n}c_{k}=\frac{n!}{(n-k)!k!}$
$\boldsymbol{\circ} \\ _{9}c_{3}(0.5)^{3}(0.5)^{6}$
$\boldsymbol{\circ} \\ _{9}c_{3}(0.5)^{3}$
$\boldsymbol{\circ} \\ _{9}c_{3}(0.5)^{3}(0.5)^{9}$
$\boldsymbol{\circ} \\ _{9}c_{6}(0.5)^{6}$

Explanation:

Step1: Identify binomial variables

$n=9$ (total flips), $k=3$ (heads, successes), $p=0.5$ (probability of heads)

Step2: Apply binomial probability formula

Substitute values into $P(k\text{ successes})=_{n}C_{k}p^{k}(1-p)^{n-k}$:
$P(3\text{ heads})=_{9}C_{3}(0.5)^{3}(1-0.5)^{9-3}=_{9}C_{3}(0.5)^{3}(0.5)^{6}$

Answer:

$_{9}C_{3}(0.5)^{3}(0.5)^{6}$