Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥2), n=6, p=0.2

Answer 1

Answer:

0.3446

Step-by-step explanation:

P(X≥2) = 1 − P(X<2)

P(X≥2) = 1 − P(X=0) − P(X=1)

P(X≥2) = 1 − ₆C₀ (0.2)⁰ (0.8)⁶ − ₆C₁ (0.2)¹ (0.8)⁵

P(X≥2) = 1 − 0.2621 − 0.3932

P(X≥2) = 0.3446

Answer 2

The probability of obtaining success more than or equal to 2 times is 0.3446.

What is Probability?

Probability is the study of the likeliness of an event to happen.

The probability of obtaining success is given as p = 0.2

n = 6

and P(X≥2) has to be determined

The binomial probability distribution is given by

$\rm P(x) = ^nC_x p^x (1 - p)^{n-x}$

1-p = 1- 0.2 = 0.8

P(X≥2) = 1 − P(X<2)

P(X<2) = P(X=0) − P(X=1)

P(X≥2) = 1 − P(X=0) − P(X=1)

P(X≥2) = 1 − ₆C₀ (0.2)⁰ (0.8)⁶ − ₆C₁ (0.2)¹ (0.8)⁵

P(X≥2) = 1 − 0.2621 − 0.3932

P(X≥2) = 0.3446

Therefore, the probability of obtaining success more than or equal to 2 times is 0.3446.

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