# A Bag Consists of 10 Balls Each Marked with One of the Digits 0 to 9. If Four Balls Are Drawn Successively with Replacement from the Bag, What is the Probability that None is Marked with the Digit 0? - Mathematics and Statistics

Sum

A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?

#### Solution

Let X denote the number of balls marked with the digit 0 among the 4 balls drawn.

Since the balls are drawn with replacement, the trials are Bernoulli trials.

X has a binomial distribution with n = 4 and p =1/10

and q = 1 - p = 1 - 1/10 = 9/10

The p.m.f. of X is given by

P(X = x) = "^nC_x  p^x  q^(n-x)

i.e. p(x) = "^4C_x (1/10)^x (9/10)^(4-x), x = 0, 1, ...,4

P(none of the ball marked with digit 0) = P(X = 0)

= p(0) = "^4C_x (1/10)^0 (9/10)^(4 - 0)

= 1xx1 xx (9/10)^4 = (9/10)^4

Hence, the probability that none of the bulb marked with digit o is (9/10)^4.

Concept: Bernoulli Trials and Binomial Distribution
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#### APPEARS IN

NCERT Class 12 Maths
Chapter 13 Probability
Q 6 | Page 577