Question

a)There are 15 broken light bulbs in a box of 100 light bulbs. A random sample of 10 bulbs is chosen without replacement. What is the probability that the sample contains exactly 5 broken bulb?

b)A car repair can be performed either on time or late, and either satisfactorily or unsatisfactorily. The probability of a repair being on time and satisfactory is 0.26. The probability of a repair being on time is 0.74. The probability of a repair being satisfactory is 0.41. What is the probability of a repair being late and unsatisfactory?

STEP BY STEP

Answer 1

a) Here n = sample size = 10

N = 100, x = number of broken light bulbs=15

Define random variable X: number of broken light bulbs.

Here random variable X follows Binomial distribution with n = 10 and p = 0.15

If random variable X follows Binomial distribution with n and p then

           x= 0,1,2,............,n

Where

                               n! = 1 * 2 * 3 * 4 *---------*n

Here we have to find P(X=5)

                     

                   

                    

                    

                     = 0.00849               (Round to 4 decimal)

The probability that the sample contains exactly 5 broken bulb is 0.00849