Question

Find the chance of drawing two blue balls in succession from a bag containing 5 red and 7 blue balls, if balls are not being replaced.
A. \[\dfrac{3}{13}\]
B. \[\dfrac{21}{64}\]
C. \[\dfrac{7}{22}\]
D. \[\dfrac{21}{66}\]

Answer 1

Hint:The probability of drawing two balls in succession when the balls are not being replaced then the probability of drawing the first ball and second ball are not the same because the total number of balls will change if not replaced so the two probabilities are not the same.

Complete step-by-step answer:
We have to find the probability of drawing two blue balls in succession from a bag containing 5 red and 7 blue balls, if balls are not being replaced
First the bag contains 5 red and 7 blue balls so the probability of drawing blue ball is
Total number of desired outcomes =7
Total number of possible outcomes=12
So, the probability of drawing blue ball is \[\dfrac{7}{12}\]. . . . . . . . . (1)
Now the ball drawn is not replaced so there are 5 red and 6 blue balls
Total number of desired outcomes =6
Total number of possible outcomes =11
So, the probability of drawing blue ball is \[\dfrac{6}{11}\]. . . . . . . . . . (2)
So, the probability of drawing two blue balls in succession from a bag containing 5 red and 7 blue balls, if balls are not being replaced is
\[\dfrac{7}{12}\times \dfrac{6}{11}=\dfrac{7}{22}\]
The correct option is option ©

Note: we know that the probability is the ratio of total number of desired outcomes to the total number of possible outcomes. If the balls are replaced then the probability of drawing two same colour balls is the same because the total number of balls won’t change.