Question

Probability question

*A box contains 3 white balls, 4 black balls, and 3 red balls. Consider selecting 3 balls at random. (a) What is the probability that you pick exactly one of each color when you select 3 balls from the box? (b) What is the probability that you pick exactly 2 white balls and 1 red ball? (c) What is the probability that at least one of the balls is white when you select 3 balls from the box?

Answer 1

a)

P(exactly one of each color)=$\binom{3}{1}\binom{4}{1}\binom{3}{1}/\binom{10}{3}$ =3*4*3/120=36/120=3/10 =0.3

b)

P(exactly 2 whlte and 1 red ball)=$\binom{3}{2}\binom{4}{0}\binom{3}{1}/\binom{10}{3}$=3*1*3/120=9/120=3/40

c)

P(at least one white ball)=1-P(0 white ball)=$\binom{3}{0}\binom{7}{3}/\binom{10}{3}$ =1-1*35/120=1-7/24=17/24

Answer 2

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