Answer to Question #173600 in Statistics and Probability for ANJU JAYACHANDRAN

Question

9b) A box contains 10 screws, 3 of which are defective. Two screws are drawn at

random. Find the probability that none of them is defective, if the sample is drawn

(i) with replacement,

(ii) without replacement.

Answer 1

Total number of screws $= 10$

Defective screws $= 3$

We have to find the probability that none of them is defective

a.) Number of ways of selecting 2 screws from 10 screws with replacement $= ^{10}C_1 \times ^{10}C_1$

Hence, The probability that none of them is defective, if the sample is drawn with replacement

$= \dfrac{^7C_1}{^{10}C_1} .\dfrac{^7C_1}{^{10}C_1}$

$= \dfrac{7}{10}.\dfrac{7}{10}$

$= \dfrac{49}{100}$

b.) Number of ways of selecting 2 screws from 10 screws without replacement $= ^{10}C_2$

Hence, The probability that none of them is defective, if the sample is drawn with replacement

$= \dfrac{^{7}C_2}{^{10}C_2}$

$= \dfrac{42}{90}$

$= \dfrac{21}{45}$