###### GATE 2022

November 8, 2023###### Question 15373 – DSSSB PGT 2021

November 8, 2023# Question 16108 – GATE 2022

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball.

First ball is drawn. What is the probability of getting an orange ball in the next draw?

Correct Answer: D

Question 8 Explanation:

Case 1: The first ball is Green

Probability of first ball is green = 3/5

If the first ball is green then we are not replacing so the probability of the second ball being orange is = 2/4.

Probability of first ball green and second ball orange is =3/5 * 2/4 = 6/20

Case 2: The first ball is orange

Probability of first ball is orange =2/5

If the first ball is orange then we are replacing it with another orange ball/ so the number balls will remain the same.

Probability of second ball is orange = 2/5

Probability of first ball is orange and second ball is also orange = 2/5*2/5 = 4/25

Therefore, Total probability = (6/20 + 4/25) = 23/50.

Probability of first ball is green = 3/5

If the first ball is green then we are not replacing so the probability of the second ball being orange is = 2/4.

Probability of first ball green and second ball orange is =3/5 * 2/4 = 6/20

Case 2: The first ball is orange

Probability of first ball is orange =2/5

If the first ball is orange then we are replacing it with another orange ball/ so the number balls will remain the same.

Probability of second ball is orange = 2/5

Probability of first ball is orange and second ball is also orange = 2/5*2/5 = 4/25

Therefore, Total probability = (6/20 + 4/25) = 23/50.

1/2

8/25

19/50

23/50

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