Answered: "Use the formula for the binomial probability distribution..."

Josalynn

Answered question

2021-09-24

Use the formula for the binomial probability distribution to find the probabilities

n = 4, p = 0.5 and x = 0, 1, 2, 3 and 4

Answer & Explanation

Alix Ortiz

Skilled2021-09-25Added 109 answers

Introduction
To find the binomial probability distribution for the given

n = 4

.
Step 2
Given data:

n = 4, p = 0.5

and

x = 0, 1, 2, 3, 4

q = 1 - p

= 1 - 0.5

= 0.5

Binomial Probability distribution:

P (X = n) = \sum_{x = 0}^{n} (b e g \in {a r r a y} {c} n ∖ x e n d {a r r a y}) p^{x} q^{n - x}

P (X = 4) = P (0) + P (1) + P (2) + P (3) + P (4)

= (b e g \in {a r r a y} {c} 4 ∖ 0 e n d {a r r a y}) {(0.5)}^{4} {(0.5)}^{4 - 0} + (b e g \in {a r r a y} {c} 4 ∖ 1 e n d {a r r a y}) {(0.5)}^{4} {(0.5)}^{4 - 1} + (b e g \in {a r r a y} {c} 4 ∖ 2 e n d {a r r a y}) {(0.5)}^{4} {(0.5)}^{4 - 2} + (b e g \in {a r r a y} {c} 4 ∖ 3 e n d {a r r a y}) {(0.5)}^{4} {(0.5)}^{4 - 3} + (b e g \in {a r r a y} {c} 4 ∖ 4 e n d {a r r a y}) {(0.5)}^{4} {(0.5)}^{4 - 4}

P (X = 4) = 0.0039 + 0.03125 + 0.09375 + 0.125 + 0.0625

= 0.3164

Conclusion
Hence, the binomial probability distribution of

P (X = 4) = 0.3164

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