To solve this problem, we will use the formula for the binomial probability, which is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the combination of n items taken k at a time
- p is the probability of success
- n is the number of trials

Given in the problem, we have p=0.5 (probability of success), n=8 (number of trials), and we are looking for the probability of exactly 1 success (k=1).

Step 1: Calculate C(n, k)
C(n, k) = n! / [k!(n-k)!]
C(8, 1) = 8! / [1!(8-1)!]
C(8, 1) = 8

Step 2: Calculate p^k
(0.5)^1 = 0.5

Step 3: Calculate (1-p)^(n-k)
(1-0.5)^(8-1) = 0.5^7 = 0.0078125

Step 4: Substitute these values into the formula
P(X=1) = C(8, 1) * (0.5^1) * (0.5^7)
P(X=1) = 8 * 0.5 * 0.0078125
P(X=1) = 0.03125

So, the probability that the experiment results in exactly 1 success is 0.031 or 3.1% when rounded to three decimal places.

Question

To solve this problem, we will use the formula for the binomial probability, which is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the combination of n items taken k at a time
- p is the probability of success
- n is the number of trials

Given in the problem, we have p=0.5 (probability of success), n=8 (number of trials), and we are looking for the probability of exactly 1 success (k=1).

Step 1: Calculate C(n, k)
C(n, k) = n! / [k!(n-k)!]
C(8, 1) = 8! / [1!(8-1)!]
C(8, 1) = 8

Step 2: Calculate p^k
(0.5)^1 = 0.5

Step 3: Calculate (1-p)^(n-k)
(1-0.5)^(8-1) = 0.5^7 = 0.0078125

Step 4: Substitute these values into the formula
P(X=1) = C(8, 1) * (0.5^1) * (0.5^7)
P(X=1) = 8 * 0.5 * 0.0078125
P(X=1) = 0.03125

So, the probability that the experiment results in exactly 1 success is 0.031 or 3.1% when rounded to three decimal places.

Knowee AI · Accepted Answer

To solve this problem, we will use the formula for the binomial probability, which is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the combination of n items taken k at a time
- p is the probability of success
- n is the number of trials

Given in the problem, we have p=0.5 (probability of success), n=8 (number of trials), and we are looking for the probability of exactly 1 success (k=1).

Step 1: Calculate C(n, k)
C(n, k) = n! / [k!(n-k)!]
C(8, 1) = 8! / [1!(8-1)!]
C(8, 1) = 8

Step 2: Calculate p^k
(0.5)^1 = 0.5

Step 3: Calculate (1-p)^(n-k)
(1-0.5)^(8-1) = 0.5^7 = 0.0078125

Step 4: Substitute these values into the formula
P(X=1) = C(8, 1) * (0.5^1) * (0.5^7)
P(X=1) = 8 * 0.5 * 0.0078125
P(X=1) = 0.03125

So, the probability that the experiment results in exactly 1 success is 0.031 or 3.1% when rounded to three decimal places.

A binomial experiment with probability of success =p0.5 and =n8 trials is conducted. What is the probability that the experiment results in exactly 1 success?Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)

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