"A. Compute the probability of x=1 using the..." was answered by our community

smileycellist2

Answered question

2021-09-16

A. Compute the probability of

x = 1

using the binomial formula.
B. Compute the binomial probability of

x = 2

using the binomial formula.

Nathalie Redfern

Skilled2021-09-17Added 99 answers

A) The formula to find binomial probability is as follows:

P (X) =_{n} C_{x} π^{x} {(1 - π)}^{(n - x)}

where, C is the combination.
n is the number of trials.
X is the random variable.

π

is the probability of success.
Here, n is 5 and

π

is 0.40.
The probability of

x = 1

using the binomial formula is calculated as follows.

P (1) =_{5} C_{1} {(0.40)}^{1} {(1 - 0.40)}^{(5 - 1)}

= \frac{5!}{1! (5 - 1)!} \times {(0.40)}^{1} \times {(0.60)}^{4}

= 5 \times 0.4 \times 0.1296

= 0.2592

Therefore, the binomial probability of

x = 1

is 0.2592.
B) The probability of

x = 2

using the binomial formula is calculated as follows.

P (2) =_{5} C_{2} {(0.40)}^{2} {(1 - 0.40)}^{(5 - 2)}

= \frac{5!}{2! (5 - 2)!} \times {(0.40)}^{2} \times {(0.60)}^{3}

= 10 \times 0.16 \times 0.216

= 0.3456

Therefore, the binomial probability of

x = 2

is 0.3456.

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