"With n=10, p=0.4, and x=3, a binomial probability..." was answered by our experts

Lauren Mullins

Answered question

2022-02-12

With n=10, p=0.4, and x=3, a binomial probability experiment is carried out. Determine the likelihood that the experiment will succeed in x out of n separate trials. Round the answer to 4 decimals.

Answer & Explanation

Skaftau0k

Beginner2022-02-13Added 10 answers

STEP-BY-STEP EXPLANATION:
Given parameters
Number of trials = 10
Probability of success (p) = 0.4
To compute the probability of x = 3 successes, we will be using the below binomial function.

chicasdelperuszp

Beginner2022-02-14Added 14 answers

Answer is

P (X = 3) = 0.2149

, because:

P (X = x) = C_{r}^{n} P^{x} {(1 - P)}^{n - x}

P (X = 3) = C_{3}^{10} \cdot {(0.4)}^{3} \cdot {(1 - 0.4)}^{10 - 3}

Recall that

P S K C_{r}^{n} = \frac{n!}{(n - r)! r!}

P (X = 3) = \frac{10!}{(10 - 3)! 3!} \cdot {(0.4)}^{3} \cdot {(0.6)}^{7}

P (X = 3) = \frac{10!}{7! 3!} \cdot {(0.4)}^{3} \cdot {(0.6)}^{7}

P (X = 3) = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1! 3 \times 2 \times 1!} \cdot {(0.4)}^{3} \cdot {(0.6)}^{7}

P (X = 3) = \frac{720}{6} \cdot {(0.4)}^{3} \cdot {(0.6)}^{7}

P (X = 3) = 120 \cdot 0.064 \cdot 0.0279936

P (X = 3) = 0.2149

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