Question

D Question 13 5 pts It is known that 10% of the calculators shipped from a particular factory are defective. Assuming a binomial distribution, determine the probability that none in a random sample of four calculators is defective? 0.2916 O 0.0010 0.3439 0.6561

Answer 1

Binomial Distribution

If 'x' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success;  ‘q’=(1-p) is given by the probability function

$P(X=r) = \binom{n}{r}p^{r}q^{n-r}$

For the given problem,

'x' random varible representing: Number of defective calculators ;

Number of trails : n : 4

p : Probability that a calculator is defective = 10/100 = 0.10

q : 1-p = 1-0.10 = 0.90

Probability that none (i.e x =0) in a random sample of four calculators is defective : p(x=0)

P(X 0) 4 ( ) × (0.10)% (0.90)4-0-1 × 1 × 0.9012 0.6561

Ans : 0.6561