Question

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads? P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 6 Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 9 Subscript 9 Baseline C Subscript 6 Baseline (0.5) Superscript 6

Answer 1

Answer:

$P(3) = ^9C_3 * 0.5^3 *0.5^6$

Step-by-step explanation:

Given

$n = 9$ --- number of flips

Required

$P(x = 3)$

The probability of getting a head is:

$p = \frac{1}{2}$

$p = 0.5$

The distribution follows binomial probability, and it is calculated using:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

So, we have:

$P(3) = ^9C_3 * 0.5^3 * (1 - 0.5)^{9-3}$

$P(3) = ^9C_3 * 0.5^3 *0.5^6$