Question

A bag contains 7 red, 5 white and 3 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is
(i) Red or White
(ii) Not black
(iii) Neither white nor black
$A.(i)\dfrac{1}{5},(ii)\dfrac{3}{7},(iii)\dfrac{7}{{13}} \\\ B.(i)\dfrac{4}{5},(ii)\dfrac{4}{5},(iii)\dfrac{7}{{15}} \\\ C.(i)\dfrac{1}{5},(ii)\dfrac{5}{8},(iii)\dfrac{7}{{17}} \\\ D.(i)\dfrac{4}{5},(ii)\dfrac{7}{9},(iii)\dfrac{7}{{19}} \\\$

Answer 1

Hint : In order to solve this problem we just have to use the formula of probability that is number of favorable outcomes upon total number of outcomes using the conditions given above.

Complete step-by-step answer :
(i) When the ball drawn is red or white when there are 7 red, 5 white and 3 black balls.
So, there are 7 red and 5 white balls so the number of favorable outcomes is
7 + 5 = 12 and the total number of outcomes is 7 + 5 + 3 = 15.
Probability that the ball drawn is red is $\dfrac{{{\text{Number}}\,{\text{of}}\,{\text{favorable}}\,{\text{outcomes}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{outcomes}}}} = \dfrac{{12}}{{15}} = \dfrac{4}{5}$ .
(ii) When the ball drawn is not black it means it is red or white from a total of 7 red, 5 white and 3 black balls.
So, there are 7 red, 5 white balls so the number of favorable outcomes is
7 + 5 = 12 and the total number of outcomes is 7 + 5 + 3 = 15.
Probability that the ball drawn is not black is $\dfrac{{{\text{Number}}\,{\text{of}}\,{\text{favorable}}\,{\text{outcomes}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{outcomes}}}} = \dfrac{{12}}{{15}} = \dfrac{4}{5}$ .
(iii) When the ball drawn is neither white nor black it means it is red from a total of 7 red, 5 white and 3 black balls.
So, there are 7 red balls so the number of favorable outcomes is 7 and total number of outcomes is 7 + 5 + 3 = 15.
Probability that the ball drawn is neither white nor black is $\dfrac{{{\text{Number}}\,{\text{of}}\,{\text{favorable}}\,{\text{outcomes}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{outcomes}}}} = \dfrac{7}{{15}}$ .
Hence, the answers is $(i)\dfrac{4}{5},(ii)\dfrac{4}{5},(iii)\dfrac{7}{{15}}$ .
So, the correct option is B.

Note : In this problem in the first case we considered only the red and white balls as it is said. While in the second case we have considered the balls except the balls which are black that means again red and white and in third case we have considered only red since the condition is not to take black and white balls. Doing this and using the basic formula of probability of number of favourable outcomes upon total number of outcomes we get the right answers.