Question

6 red and 4 black balls in a box. how many ways can you choose 3 black balls from box?What is the probability that none are chosen red? What is the probability that out of three at least one is red? What is the probability two are red and one is black?

Answer 1

Assuming that the balls are selected at random:
The number of ways of choosing 3 black balls out of the 4 black balls is C(4, 3).
The probability that none of the sample of 3 is red is given by:
\[\large P(none\ are\ red)=\frac{C(4, 3)}{C(10, 3)}\]
The probability that out of three at least one is red is given by:
\[\large P(at\ least\ one\ is\ red)=1-P(none\ is\ red)\]