Probability question

Question

There are 3 red, 5 blue and 2 yellow balls in a box. Two balls are drawn at random without replacing the first one. Find the probability that

i) at least one is yellow

ii) Both of them are not red

Answer 1

Balls in the box

RED---3

BLUE-----5

YELLOW ----2

Total ---------10

i) Probability that 1st ball drawn is not yellow  will be 8/10

Probability that 2nd ball drawn without replacement is not also yellow will be 7/10

As the events are idepedent ,then probability that both the balls drawn one after another is not yellow will be 8/10×7/9=28/45

Hence probability of drawing at least one yellow ball will be = 1-28/45=17/45.

ii) Probability that 1st ball drawn is red will be =3/10

Probability that 2nd ball drawn without replacement of first red ball is also red will be 2/9

Then probability that both are not red  wil be

=1-3/10×2/9=1-1/15=14/15

Comments

Thanks for the help sir.