Question

Consider a binomial experiment with n = 4 trials where the probability of success on a single trial is p = 0.25. (For each answer, enter a number. Round your answers to three decimal places.) (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.

Answer 1

Answer:

(a) $\approx$ 0.32

(b) $\approx$ 0.68

Step-by-step explanation:

It is given that a binomial experiment is carried out.

n = 4 trials

Probability of success, p = 0.25

We know that in a binomial experiment:

Probability of success + Probability of failure = 1

p + q = 1

So, q = 1 - 0.25 = 0.75

Probability of 'r' number of successes in 'n' trials of a binomial experiment is given as:

$P(r=x) = _nC_x\times p^x(q)^{n-x}$

(a) P(r = 0) = ?

Putting values of x = 0, p and q:

$P(r=0) = _4C_0\times (0.25)^0\times (0.75)^{4-0}\\P(r=0) = 1\times 1\times (0.75)^{4}\\P(r=0) \approx 0.32$

(b) Find P(r ≥ 1)  = ?

Using complement rule:

P(r =0 ) + P(r ≥ 1)  = 1

0.32 + P(r ≥ 1)  = 1

P(r ≥ 1)  = 1 - 0.32

P(r ≥ 1)  = 0.68

So, the answer are:

(a) $\approx$ 0.32

(b) $\approx$ 0.68