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Q.

A bag contains white, black, and red balls only. A ball is drawn at random from the bag. The probability of getting a white ball is 3 10   and that of a black ball is 2 5  . Find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.


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a

Probability = 4 10  , Total balls = 11

b

Probability = 1 10  , Total balls = 40

c

Probability = 2 10  , Total balls = 45

d

Probability = 3 10  , Total balls = 50 

answer is D.

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Detailed Solution

It is given that a bag contains white, black, and red balls only.
The probability of white ball is 3 10 .  
The probability of black ball is 2 5  .
We know that, the sum of the different probability in a particular observation is always equal to 1.
  P(B)+P(W)+P(R)=1 ⇒P(R)+ 3 10 + 2 5 =1 ⇒P(R)=1− 3 10 − 2 5 ⇒P(R)= 3 10  
Hence, the probability of getting a red ball is 3 10 .  
Number of black balls in the bag = 20.
Probability of getting black ball,
  P(B)= n(B) n(T)  .
Where n(B)(Number of black balls) = 20 and n(T) = total number of balls.
Thus, n(T)= n(B) P(B)  
⇒n(T) = 20 2 5 ⇒n(T) =20 5 2 ⇒n T =50  
Hence, the probability of getting red balls is 3 10   and the total balls in the bag is 50.
Therefore, the correct answer is option (4).
 
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A bag contains white, black, and red balls only. A ball is drawn at random from the bag. The probability of getting a white ball is 3 10   and that of a black ball is 2 5  . Find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.