A bag contains 9 white and 3 red balls. Two are drawn in succession. What is the probability that one is white and the other is red
Answers
probability of white is 3/4
and red is 3/11
#as one white ball has already drawen from bag
Answer:
The given question is based on probability. Let us see how to calculate the answer in the explanation.
Step-by-step explanation:
Given: A bag that contains 9 white and 3 red balls.
To Find: The probability that one ball is white and one is red if two balls are drawn from the bag in succession, that means there is no replacement.
Now, the bag contains 9 white and 3 red balls. Hence, total number of balls = 9+3 = 12 balls.
There are total 12 balls in the bag.
We know probability =
Number of favorable outcomes / Total number of outcomes
Now, we are not told whether the white ball is drawn first or the red. We are just asked to give the probability that one is white and other is red. Hence, there will be two outcomes.
1. When white ball is drawn first and then the red:
Probability of white ball being drawn first = 9/12
Probability of red ball being drawn second = 3/11
Hence, total probability of first ball being white and other being red in this case = (9/12)×(3/11)
= 27/132
2. When red ball is drawn first and then the white:
Probability of red ball being drawn first = 3/12
Probability of white ball being drawn second = 9/11
Total probability of first ball being red and other being white:
= (3/12)×(9/11)
= 27/132
Therefore, total probability of one ball being red and other being white
= 27/132 + 27/132
= 54/132
The answer is 54/132.