Use a binomial probabilities table to find the probability of x successes given the probability p of success on a given trial. n=4​, x=4​, p=

Question

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use a binomial probabilities table to find the probability of x successes given the probability p of success on a given trial.

n=4​,

x=4​,

p=0.60

P(4)= ?

​(Round to three decimal places as​ needed.)

Answer 1

When n=4 the probability coefficients are 1 4 6 4 1. These are applied to p and 1-p as follows:

p^4 4p^3(1-p) 6p^2(1-p)^2 4p(1-p)^3 (1-p)^4 These terms sum to 1 being the expansion of (p+(1-p))^4=1.

These can be evaluated for p=0.60:

4/4: 0.60^4=0.1296

3/4: 4*0.60^3*0.40=0.3456

2/4: 6*0.60^2*0.40^2=0.3456

1/4: 4*0.60*0.40^3=0.1536

0/4: 0.40^4=0.0256

From this table, the chances of 4/4 or 4 successes out of 4=0.130.