To solve this problem, we can use the formula for the binomial probability:

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, n=8, and we're looking for k=2.

First, calculate C(n, k) = C(8, 2). This is the number of ways you can get 2 successes in 8 trials. Using the formula for combinations, we get C(8, 2) = 8! / [2!(8-2)!] = 28.

Next, calculate p^k = (0.5)^2 = 0.25.

Then, calculate (1-p)^(n-k) = (1-0.5)^(8-2) = (0.5)^6 = 0.015625.

Finally, multiply these three values together to get the probability:

P(X=2) = 28 * 0.25 * 0.015625 = 0.109375.

So, the probability that the experiment results in exactly 2 successes is approximately 0.109, which is closest to the first option.

Question

To solve this problem, we can use the formula for the binomial probability:

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, n=8, and we're looking for k=2.

First, calculate C(n, k) = C(8, 2). This is the number of ways you can get 2 successes in 8 trials. Using the formula for combinations, we get C(8, 2) = 8! / [2!(8-2)!] = 28.

Next, calculate p^k = (0.5)^2 = 0.25.

Then, calculate (1-p)^(n-k) = (1-0.5)^(8-2) = (0.5)^6 = 0.015625.

Finally, multiply these three values together to get the probability:

P(X=2) = 28 * 0.25 * 0.015625 = 0.109375.

So, the probability that the experiment results in exactly 2 successes is approximately 0.109, which is closest to the first option.

Knowee AI · Accepted Answer

To solve this problem, we can use the formula for the binomial probability:

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, n=8, and we're looking for k=2.

First, calculate C(n, k) = C(8, 2). This is the number of ways you can get 2 successes in 8 trials. Using the formula for combinations, we get C(8, 2) = 8! / [2!(8-2)!] = 28.

Next, calculate p^k = (0.5)^2 = 0.25.

Then, calculate (1-p)^(n-k) = (1-0.5)^(8-2) = (0.5)^6 = 0.015625.

Finally, multiply these three values together to get the probability:

P(X=2) = 28 * 0.25 * 0.015625 = 0.109375.

So, the probability that the experiment results in exactly 2 successes is approximately 0.109, which is closest to the first option.

A binomial experiment with probability of success p=0.5 and n=8 trials is conducted. What is the probability that the experiment results in exactly 2 successes?2 points0.1090.1390.1690.199

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