Questions: Assume that a procedure yields a binomial distribution with n=8 trials and a probability of success of p=0.60. Use a binomial probability table to find the probability that the number of successes x is exactly 1.

Solution Steps

We are given a binomial distribution with the following parameters:

• Number of trials \( n = 8 \)
• Probability of success \( p = 0.60 \)
• Probability of failure \( q = 1 - p = 0.40 \)

To find the probability of exactly \( x = 1 \) success, we use the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

Substituting the values:

\[ P(X = 1) = \binom{8}{1} \cdot (0.60)^1 \cdot (0.40)^{8-1} \]

Calculating \( \binom{8}{1} = 8 \):

\[ P(X = 1) = 8 \cdot 0.60 \cdot (0.40)^7 \]

Calculating \( (0.40)^7 \):

\[ (0.40)^7 \approx 0.0016 \]

Thus,

\[ P(X = 1) \approx 8 \cdot 0.60 \cdot 0.0016 = 0.00768 \]

Rounding to four significant digits, we find:

\[ P(X = 1) \approx 0.0079 \]

Final Answer