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Calculate the probability of x = 3 successes in n = 6 trials of a binomial experiment with probability of success p = 0.4. a. 1.659 b. 0.821 c. 0.276 d. 0.014

User Valeriya
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6 votes

Answer:

To calculate the probability of exactly x = 3 successes in n = 6 trials of a binomial experiment with a probability of success p = 0.4, you can use the binomial probability formula:

P(X = x) = (n choose x) * p^x * (1 - p)^(n - x)

Where:

- n is the number of trials (in this case, n = 6).

- x is the number of successes you want to calculate the probability for (in this case, x = 3).

- p is the probability of success on a single trial (in this case, p = 0.4).

- (n choose x) represents the number of combinations of n items taken x at a time and can be calculated as C(n, x) = n! / (x! * (n - x)!), where "!" denotes factorial.

Now, let's calculate it step by step:

1. Calculate (n choose x):

C(6, 3) = 6! / (3! * (6 - 3)!) = (6 * 5 * 4) / (3 * 2 * 1) = 20

2. Calculate p^x:

p^3 = (0.4)^3 = 0.064

3. Calculate (1 - p)^(n - x):

(1 - p)^(6 - 3) = (1 - 0.4)^3 = (0.6)^3 = 0.216

4. Now, plug these values into the formula:

P(X = 3) = 20 * 0.064 * 0.216

5. Calculate the final result:

P(X = 3) ≈ 0.27648

So, the probability of getting exactly 3 successes in 6 trials with a success probability of 0.4 is approximately 0.27648. The closest option is (c) 0.276.

Explanation:

User Prasoon Saurav
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