Book: RD Sharma - Mathematics (Volume 2)

Chapter: 33. Binomial Distribution

Subject: Maths - Class 12th

Q. No. 33 of Exercise 33.1

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

33
Suppose that a radio tube inserted into a certain type of set has probability 0.2 of functioning more than 500 hours. If we test 4 tubes at random what is the probability that exactly three of these tubes function for more than 500 hours?

Let p be the probability of the tube to function for more than 500 hours.

This probability is given as 0.2.

p = 0.2

If p is the probability of the tube to function for more than 500 hours, then q is the probability of the tube to not function for more than 500 hours.

p + q = 1

q = 1 – p

Let X denote a random variable that represents the number of the tube that can function for more than 500 hours out of the total 4 tubes.

And let n denote the total number of tube taken in the sample, that is, 4.

Then binomial distribution for r tube to function more than 500 hours out of 4 tubes is given by,

P (X = r) = nCrprqn-r

Putting n = 4, and above, we get

We need to find the probability that exactly 3 tubes will function for more than 500 hours.

So, put r = 3. We get

Thus, the probability that exactly 3 tubes will function for more than 500 hours is .

26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54