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

The expression represents the probability of getting exactly 3 heads is $\rm= ^9C_3 \times (0.5)^3\times (0.5)^{6}$.

Given

Aron flips a penny 9 times.

We have to determine

Which expression represents the probability of getting exactly 3 heads?

What is binomial distribution?

The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.

The binomial probability formula shown has variables which represent:

$\rm= ^nCr \times p^r\times (1-p)^{n-r}$

Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).

r is the number we want to find (here, we want the probability of 3 heads, so r = 3).

p is the probability of success (here, success means getting heads.

So, in a coin flip the probability of heads is always 1/2, so p = 1/2).

Therefore,

The expression represents the probability of getting exactly 3 heads is;

$\rm= ^nCr \times p^r\times (1-p)^{n-r}\\\\\rm= ^9C3 \times (0.5)^3\times (1-0.5)^{9-3}\\\\= ^9C3 \times (0.5)^3\times (0.5)^{6}$

Hence, the expression represents the probability of getting exactly 3 heads is $\rm= ^9C_3 \times (0.5)^3\times (0.5)^{6}$.

To know more about Binomial Distribution click the link given below.

brainly.com/question/7236644