Question

Determine the following probabilities. a. For \( n=2 \) and \( \π=0.14 \), what is \( P(X=0) \) ? b. For \( n=9 \) and \( \π=0.40 \), what is \( P(X=8) \) ? c. For \( n=9 \) and \( \π=0.60 \), what"

A) 0.14
B) 0.86
C) 0.0252
D) 0.9748

Answer 1

The probability of getting zero successes (P(X=0)) in a binomial experiment where n=2 and π=0.14 is approximately 0.7396, calculated using the binomial probability formula.

The student's question is related to probability and specifically to calculating the probability of a certain number of successes in a binomial experiment. To find P(X=0) for n=2 and π=0.14, we use the binomial probability formula:

P(X=k) = C(n, k) * π^k * (1-π)^(n-k)

For P(X=0), substitute the values:

P(X=0) = C(2, 0) * 0.14^0 * (1-0.14)^2 = 1 * 1 * 0.86^2 = 0.7396

So, P(X=0) when n=2 and π=0.14 is approximately 0.7396.