### two marbles are selected at random from a box containing 5 red, 7 white and...

two marbles are selected at random from a box containing 5 red, 7 white and 8 blue marbles one after the other without replacement. find the probability that:
a) both are red
b) one is white and the other Is blue
c) both are of the same colour.?

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Zealot
1 month ago
red=5
white=7
blue=8
T=5+7+8=20 marbles

a)both are red=RR=5/20 * 4/19
=1/4 *4/19
=1/19

b)pr(WB or BW)=(7/20 * 7/19)+(8/20 * 6/19)
=49/380 + 48/380
=(49+48)/380
=97/380

c)pr(BB or WW or RR)=(8/20 *7/19)+(7/20 *6/19)+(5/20 * 4/19)
=56/380 +42/380 +20/380
=(56+42+20)/380
=118/380
=59/190
Follow
• Tomiwafolu: a) possibility that both are red;
step 1 :- possibility that 1 is red =>
total marbles : 5+7+8 = 20
Red: 5/20 = 1/4
step 2 :- possibility that both are red;
5/20 × 4/19 = 1/4 × 4/19 = 1/19

b) possibility that one is white =>
7/20
possibility that one is blue =>
8/20
possibility that one is blue and one is white:
7/20 × 8/19= 7/5 × 2/19 =14/95

c) possibility that both are red =>
5/20 × 4/19 = 1/4 × 4/19 = 1/1 × 1/19 = 1/19
possibility that both are blue =>
8/20 × 7/19 = 2/5 × 7/19 = 14/95
possibility that both are white:
7/20 × 6/19 = 7/10 × 3/19 = 21/190
possibility of both being the same colour:
1/19 + 21/190 + 14/95 = 10 + 21 + 28
------------------ =
190
59/190

Note: the question states without replacement which makes it exclusive and not independent
1 month ago
• Zealot: b)pr(WB or BW)
=(7/20 * 8/19)+(8/20 * 7/19)
=56/380 + 56/380
=56+56/380
=112/380
=28/95
1 month ago