Question

A bag containing 8 red balls and 5 green balls . Two balls are drawn without replacement (simultaneously) from the bag . Find the probability that both the balls drawn are green .

Answer 1

Probability that both the balls were drawn are green = (5/13) * (4/12)

                                                                                         = 5/39

Answer 2

Given,

In a bag;

Number if red balls = 8

Number of green balls = 5

To find,

If two balls are drawn without replacement (simultaneously) from the bag, then the probability that both the balls drawn are green.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

The probability of occurrence of a favorable event = P (favorable event)

= (Total number of occurrence of the favorable event) / (Total number of occurrence of all possible events)

= (Total number of occurrence of the favorable event) / (Total number of trials)

Initially, the total number of balls in the bag = 8+5 = 13

Now, after the first ball drawn is green;

number of balls left = 13-1 = 12

number of red balls = 8

the number of green balls = 5-1 = 4.

Now,

The probability that both the balls drawn are green

= (probability that the first ball drawn is green) x (probability that the first ball drawn is green)

= (5/13)(4/12)

= 5/39

Hence, the probability that both the balls drawn are green is equal to 5/39.