Probability?

Question

Two bags contain coloured balls.
Bag A contains 5 black balls and 3 white balls.
Bag B contains 6 black balls and 5 white balls.
A ball is drawn at random from Bag A. If a black ball is drawn from Bag A, it will be put back into Bag A. If a white ball is drawn from Bag A, the white ball drawn will be put into Bag B. A second ball is then drawn at random from Bag B.

(i) Calculate the probability that the two balls drawn are both black.
Ans: 15/44

(ii) Calculate the probability that the two balls drawn are of a different colour.
Ans: 83/176


Please show your workings clearly and explain...thank you.

Answer 1

(i) prob that first is black = 5 / 8
prob that second is black = 6 / 11

multiply them to get

30 / 88
=15/44

(ii)chance that first is black = 5 / 8
chance that second is white = 5 / 11
multiply and get - 25 / 88
or

chance that first is white = 3 / 8
chance that second is black = 6 / 12 = 1 / 2
3/8 * 1/2
= 3 / 16

add together
25/88 + 3/16
cross multiply blah
=(400+264)/1408
=664/1408
=83/176

Answer 2

i) P(BB) = 5/8 * 6/11 = 30/88=15/44 Since if the first ball drawn is black the experiments are independent all you need to do is multiply the odds of black in bag a and the odds of black in bag b.

ii) This one will be the sum of P(BW) and P(WB) as stated in problem i) if black is drawn first then it is number of wanted balls in a divided by total balls is a, multiplied by number of wanted balls in be divided by total balls in b or 5/8*5/11=25/88
However to find P(WB) we need to remember the white ball from bag a is put into bag b, so we have the number of wanted balls in a divided by total balls is a, multiplied by number of wanted balls in be divided by total balls in b(including the newly added white ball) or 3/8*6/12=18/96= 3/16

so we have 25/88 + 3/16 = 50/176 + 33 / 176 = 83/176

Hope This Helps,

MathIsFun

Answer 3

Bag A_______Bag B
5B,3W______6B,5W

Part (i)
P (two black) = 5/8 x 6/11 = 30/88 = 15/44

Part (ii)
P (W,B) = 3/8 x 1/2 = 3/16
P (B,W) = 5/8 x 5/11 = 25/88
P(different colour)
= 3/16 + 25/88
= 33/176 + 50/176
= 83/176

Answer 4

i)
p(black in bag A )=5/(3+5)=5/8
p(black in bag B)=6/(6+5)=6/11
p(the two balls drawn are both black)
=(5/8) * (6/11)
=30/88
=15/44

ii)
p(black,white)=(5/8) * (5/11)
=25/88

p(white,black)=(3/8)*(6/(11+1))
=3/16

p(two balls drawn are of a different colour)
=25/88 + 3/16
=83/176