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

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

We want to find the probability of 1 or fewer successes, so we need to find P(X=0) and P(X=1) and then add these probabilities together.

1. Calculate P(X=0):
Here, k=0. So, we plug in the values into the formula:
P(X=0) = C(11, 0) * (0.32^0) * ((1-0.32)^(11-0))
= 1 * 1 * (0.68^11)
= 0.68^11
= 0.00057 (approximately)

2. Calculate P(X=1):
Here, k=1. So, we plug in the values into the formula:
P(X=1) = C(11, 1) * (0.32^1) * ((1-0.32)^(11-1))
= 11 * 0.32 * (0.68^10)
= 0.0035 (approximately)

3. Add P(X=0) and P(X=1) to get the final probability:
P(X

Question

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

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

We want to find the probability of 1 or fewer successes, so we need to find P(X=0) and P(X=1) and then add these probabilities together.

1. Calculate P(X=0):
   Here, k=0. So, we plug in the values into the formula:
   P(X=0) = C(11, 0) * (0.32^0) * ((1-0.32)^(11-0))
   = 1 * 1 * (0.68^11)
   = 0.68^11
   = 0.00057 (approximately)

2. Calculate P(X=1):
   Here, k=1. So, we plug in the values into the formula:
   P(X=1) = C(11, 1) * (0.32^1) * ((1-0.32)^(11-1))
   = 11 * 0.32 * (0.68^10)
   = 0.0035 (approximately)

3. Add P(X=0) and P(X=1) to get the final probability:
   P(X<=1) = P(X=0) + P(X=1)
   = 0.00057 + 0.0035
   = 0.00407

So, the probability that the experiment results in 1 or fewer successes is approximately 0.00407 or 0.407%.

Knowee AI · Accepted Answer

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

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

We want to find the probability of 1 or fewer successes, so we need to find P(X=0) and P(X=1) and then add these probabilities together.

1. Calculate P(X=0):
   Here, k=0. So, we plug in the values into the formula:
   P(X=0) = C(11, 0) * (0.32^0) * ((1-0.32)^(11-0))
   = 1 * 1 * (0.68^11)
   = 0.68^11
   = 0.00057 (approximately)

2. Calculate P(X=1):
   Here, k=1. So, we plug in the values into the formula:
   P(X=1) = C(11, 1) * (0.32^1) * ((1-0.32)^(11-1))
   = 11 * 0.32 * (0.68^10)
   = 0.0035 (approximately)

3. Add P(X=0) and P(X=1) to get the final probability:
   P(X<=1) = P(X=0) + P(X=1)
   = 0.00057 + 0.0035
   = 0.00407

So, the probability that the experiment results in 1 or fewer successes is approximately 0.00407 or 0.407%.

A binomial experiment with probability of success p=0.32 and n=11 trials is conducted. What is the probability that the experiment results in 1 or fewer successes?

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