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3 votes
Find the probability of exactly three

successes in eight trials of a binomial
experiment in which the probability of
success is 45%.
Enter k, or the number of successes.
D
k = [ ? ]

User CorayThan
by
8.5k points

1 Answer

6 votes

Answer:

Explanation:

To find the probability of exactly three successes in eight trials of a binomial experiment with a probability of success of 45%, we can use the binomial probability formula.

The binomial probability formula is given by:

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

Where:

P(k) is the probability of k successes,

C(n, k) is the number of combinations of n items taken k at a time (also known as "n choose k"),

p is the probability of success,

n is the total number of trials.

In this case, k is 3 (number of successes), p is 0.45 (probability of success), and n is 8 (total number of trials).

Plugging these values into the formula, we get:

P(3) = C(8, 3) * 0.45^3 * (1 - 0.45)^(8 - 3)

Using the combination formula, C(8, 3) = 8! / (3! * (8 - 3)!) = 56.

P(3) = 56 * 0.45^3 * 0.55^5

Calculating this, we find:

P(3) ≈ 0.3113

Therefore, the probability of exactly three successes in eight trials with a 45% probability of success is approximately 0.3113 or 31.13%.

User Mitchf
by
8.6k points