Question

Using the binomial distribution, if n=5 and p=0.3, find P(x=5).

Options:
a) 0.00243
b) 0.36015
c) 0.16807
d) 0.00247

Answer 1

The probability of getting 5 successes in 5 trials with a success probability of 0.3 is 0.00243. Option A is answer.

Step-by-step explanation:

Calculation of P(x=5)

Step 1: Identify the formula:

For a binomial distribution with n trials and a probability of success p, the probability of getting x successes is given by:

P(x) = (nCx) * p^x * (1-p)^(n-x)

Step 2: Substitute the given values:

n = 5 (number of trials)

p = 0.3 (probability of success)

x = 5 (number of successes)

Step 3: Calculate the binomial coefficient:

nCx = 5C5 = 1 (combination of 5 successes out of 5 trials)

Step 4: Calculate each term:

p^x = 0.3^5 = 0.00243

(1-p)^(n-x) = (1-0.3)^(5-5) = 0.7^0 = 1

Step 5: Multiply the terms:

P(x) = 1 * 0.00243 * 1 = 0.00243

Therefore, the probability of getting 5 successes in 5 trials with a success probability of 0.3 is 0.00243.

Therefore, the correct answer is a) 0.00243.