"a) Compute the probability of x=2 using the..." was answered by our community

facas9

Answered question

2021-09-30

a) Compute the probability of

x = 2

using the binomial formula.
b) Compute the probability of

x = 3

using the binomial formula.

smallq9

Skilled2021-10-01Added 106 answers

a) The formula to find the 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.
The probability of

x = 2

using the binomial formula is calculated as follows.

P (X = 2) =_{4} C_{2} {(0.25)}^{2} {(1 - 0.25)}^{(4 - 2)}

= \frac{4!}{2! (4 - 2)!} \times {(0.25)}^{2} \times {(0.75)}^{2}

= 6 \times 0.0625 \times 0.5625

= 0.2109

Therefore, the probability of

x = 2

is 0.2109.
b) The probability of

x = 3

using the binomial formula is calculated as follows.

P (X = 3) =_{4} C_{3} {(0.25)}^{3} {(1 - 0.25)}^{(4 - 3)}

= \frac{4!}{3! (4 - 3)!} \times {(0.25)}^{3} \times {(0.75)}^{1}

= 4 \times 0.0156 \times 0.75

= 0.0469

Therefore, the probability of

x = 3

is 0.0469.

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