Answer:
<u> The probability of exactly 3 successes in 6 trials of a binomial experiment in which the probability of success if 50%, is:</u>
<u>31.3% (Rounding to the nearest tenth)</u>
Step-by-step explanation:
With the information provided, P = 0.5, n = 6 and k = 3, we can build the binomial distribution table, this way:
Binomial distribution (n=6, p=0.5)
f(x) F(x)
x Pr[X = x] Pr[X ≤ x]
0 0.0156 0.0156
1 0.0938 0.1094
2 0.2344 0.3438
3 0.3125 0.6563
4 0.2344 0.8906
5 0.0938 0.9844
6 0.0156 1.0000
Under the first column we have the probabilities of success of every value from 0 to 6, and under the second column we have the values for answering the question at least how much probability we have of any number of successes. Our question is exactly 3 successes in 6 trials and we see that value under the first column: 0.3125.
Therefore, the probability of exactly 3 successes in 6 trials of a binomial experiment in which the probability of success if 50%, is:
<u>31.3% (Rounding to the nearest tenth)</u>
Let's recall that the formula for calculating the probability of exact successes is:
P(k out of n) = (n!/k!(n-k)!) * (p∧k*(1-p)∧(n-k))
in our case p=0.5, n=6, k=3
(n!/k!(n-k)!) = 20 and (p∧k*(1-p)∧(n-k)) = 0.015625
20 * 0.015625 = 0.3125
