Math Help - probability

Bag A contains 5 similar balls, 3 red and 2 black and bag B has 4 red and 5 black balls. a ball is drawn form A and places in B and then a ball is drawn from B and places in A. what is the chance that if a ball is now drawn form A, it will be red? and if this ball is red, what is the probability that the first two balls are also red?

Originally Posted by alexandrabel90

Bag A contains 5 similar balls, 3 red and 2 black and bag B has 4 red and 5 black balls. a ball is drawn form A and places in B and then a ball is drawn from B and places in A. what is the chance that if a ball is now drawn form A, it will be red? and if this ball is red, what is the probability that the first two balls are also red?

hi

This is a conditional probability problem

(1) Let R be red and P be events of being drawn from A

P(R|P)=P(P n R)/P(P)

=(3/14)/(5/14)

=3/5

(2) Let R be events of first ball being red , and Q be events of second ball being red

P(Q|R)=P(R n Q)/P(R)

=(5/10)/(3/5)

=5/6

Since the first red ball is drawn from A , the second ball (unknown colour) will be drawn from B according to the question . Now , the number of red balls increases by 1 in B , making 5R 5B and 2R 2B in A .

the answer for that should be 143/250 and 45/143 i think