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

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads?

Answer: A

Explanation:

Answer 2

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

Explanation:

Given

`n = 9` --- number of flips

Required

`P(x = 3)`

The probability of getting a head is:

`p = (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`