SOLUTION: A box contains 8 blue marbles, 4 red marbles, 3 green marbles. A. if three marbles are selected at random, what is probability that all three marbles will be blue marbles B. i

Question 267894: A box contains 8 blue marbles, 4 red marbles, 3 green marbles.
A. if three marbles are selected at random, what is probability that all three marbles will be blue marbles
B. if three marbles are selected at random, what is the probability that one of each color marble will be selected.
C. if 11 marbles are selected at random, what is the probability that no red marbles will be selected.
D. if six marbles are selected at random, what is the probability that two of each color marble will be selected?

Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
A box contains 8 blue marbles, 4 red marbles, 3 green marbles.
Total number of balls = 8+4+3 = 15
A. if three marbles are selected at random,what is probability that all three marbles will be blue marbles
Total number of ways = 15C3 = (15*14*13) / (1*2*3) = 455
Out of 5 blue balls 3 can be selected in 5C3 ways.
The number of favourable ways = 5C3 = (5*4*3)/(1*2*3)=10
The probability that all three marbles will be blue marbles = 10/455 = 2/91
B. if three marbles are selected at random,what is probability that one of each colour be selected .
Total number of ways = 15C3 = (15*14*13) / (1*2*3) = 455
Out of 8 blue balls 1 can be selected in 8 ways,Out of 4 red balls 1 can be selected in 4 ways,Out of 3 green balls 1 can be selected in 3 ways,
The number of favourable ways = 5C3 = (8*4*3)=96
The probability that all three marbles will be blue marbles = 96/455
C. if 11 marbles are selected at random, what is the probability that no red marbles will be selected
Total number of ways = 15C11 = 15C4 = (15*14*13*12)/(1*2*3*4) = 1365
Leaving the 4 red balls there are 8 blue and 3 green balls.
So Out of 11 (blue balls+green ) 11 can be selected in 1 way.
The number of favourable ways = 1
The probability that all 11 marbles will be blue marbles or green = 1/455
D. if six marbles are selected at random, what is the probability that two of each color marble will be selected?

Total number of ways = 15C6 = (15*14*13*12*11*10)/(1*2*3*4*5*6) = 5005
Out of 8 blue balls 2 can be selected in 8C2 ways,Out of 4 red balls 2 can be selected in 4C2 ways,Out of 3 green balls 2 can be selected in 3C2 ways,
The number of favourable ways = (8C2)*(4C2)*(3C2)=504
The probability that that two of each color marble will be selected
= 504/5005

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