A box contains 3 red marbles, 6 blue marbles, and 1 white marble. The marbles are selected at random, one at a time, and are not replaced. Find the probability.
P(blue and red)
P(white and blue)
P(red and white)
P(red and white and blue)
P(red and red and blue)
P(red and blue and blue)
P(red and red and red)
P(white and blue and blue)
P(white and red and red)

I do this one and leave the other as excersises.

How many ways are there of choosing 3?
In total we have 3+6+1=10.
Thus, 10C3=120

How many ways of choosing 1 white, 1C1=1
Similarly, red: 3C1=3 and blue: 6C1=6.
Thus, there are (1)(3)(6)=18 different ways of choosing red,white and blue.

The probability therefore is,
18/120=3/20=15%

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"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran

Hello, valo4212!


From the wording of the problems,
. . I assume that the colors are drawn in that order.

. . . . . . . . . . . . . . . 6 . .3 . . . . .1
(1) .P(B and R) . = . --- · --- . = . --
. . . . . . - - - . . . . . 10 . .9 . . . . .5


. . . . - - - . . . . . . . . 1 . . 6 . . . . 1
(2) .P(W and B) . = . --- . -- . = . ---
. . . . . . - - - . . . . . .10 . .9 . . . .15


Want to try the rest of them now?