Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that i. both balls are red, ii. first ball is black and second is red, iii. One of them is black and other is red.

Answer

N/a

Explanation

(i) Here `n(S)=.^(18)C_(2)`
`n(E)=` Favourable outcomes of drawing two black balls `=.^(10)C_(2)`
`:. P(E)=(n(E))/(n(S))=(.^(10)C_(2))/(.^(18)C_(2))=(10xx9)/(18xx17)=5/17`
(ii) Probability of drawing first black and second red ball without substitution `=(.^(10)C_(1))/(.^(18)C_(1))xx(.^(8)C_(1))/(.^(17)C_(1))`
`=10/18xx8/17=40/153`
(iii) Probability of drawing one black and one red
ball `=(.^(10)C_(1)xx.^(8)C_(1))/(.^(18)C_(1))=80/153`