Finite Question

Question

Assume that each bag contains 6 balls. Bag a contains 3 red and 3 white, while bag b contains 2 red, 3 white, and 1 blue. You randomly select one ball from bag a, note the color, and place the ball in bag b. You then select a ball from bag b at random and make note of its color.


(1) What is the probability that both balls are red?

(2) What is the probability that both balls are red given that the first ball you drew was red?

Answer 1

3 red 3 white in bag a

2 red 3 white 1 blue in bag b

select 1 randomly from a and put it in b

select 1 randomly from b. what is probability both were red?

half the balls in bag a are red, then when a red ball is transferred to bag b, bag b then has 3 red out of 7 total balls. 1/2 chance of getting a red, then 3/7 chance of a 2nd red:

1/2 x 3/7 = 3/14 = about 21% chance

what is probability 2nd draw is red if 1st was red? 3/7 = about 43% chance

3 are red now in 2nd bag out of 7 total balls in 2nd bag

Answer 2

(1) Probability that both balls are red = 

 

Probability of ball drawn from bag A is red * Probability of ball drawn from bag B is red

 

= (3/6) * (3/7)

 

= 3/14

 

Explanation: in bag 1 we have 3 red out of 6 total balls hence probability of getting a red ball = 3/6 we now keep this red ball in bag b, now in bag b we have 3 red balls out of 7 total balls hence probability of picking a red ball is 3/7

 

(2) Probability that both balls drawn are red  given that first ball you drew was red

 

= 3/7 (since we know ball drawn from bag a is red so we just need to find the probability that ball drawn from bag b is also red: = 3/7)