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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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Answers (4)

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
  • 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
    Like 3    Dislike 0   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
    Like 2    Dislike 0   1 month ago
  • Zealot: #tomiwafolu thanks for your reply,but that b you don't complete your answer


    note:the question said one blue and one white.The question does not specify that the first one is blue and the second one is white,but it was stated that 1blue and 1white
    Like 1    Dislike 0   1 month ago
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