SKILLS

17-20 Probability Distribution A binomial experiment with probability of success p is performed n times. (a) Make a table of the probability distribution. (b) Draw a probability histogram.

n = 4 , p = 0.5

(a)

To make:

The table of probability distribution.

Approach:

The probability of getting exactly r successes in n independent trials of the experiment is,

P(r successes in n trials)=C(n,r)pr(1−p)n−r=n!r!(n−r)!pr(1−p)n−r ...... (1)

The probability of failure is given as,

P(failure)=1−p ……(2)

Calculation:

The number of independent trial is,

n=4

The probability of success is,

p=0.5

Calculate the probability of 0 success.

Substitute 0 for r, 0.5 for p and 4 for n in equation (1).

P(0)=4!0!(4−0)!(0.5)0(1−0.5)4−0=1(1)(0.0625)=0.0625=116

Calculate the probability of 1 success.

Substitute 1 for r, 0.5 for p and 4 for n in equation (1).

P(1)=4!1!(4−1)!(0.5)1(1−0.5)4−1=4(0.5)(0.125)=0.25=14

Calculate the probability of 2 success.

Substitute 2 for r, 0.5 for p and 4 for n in equation (1).

(b)

To draw:

The probability histogram.