Question

Determine the required probabilities.

Suppose you are to draw a ball from a box consisting of 2 red, 2 blue and 2 yellow balls twice.Let R be the random variable representing the number of Red. What is the probability of getting atleast 1 red?

Answer 1

$$P(R\ge1)=1-P(R=0)$$

$$=1-\dfrac{\dbinom{2+2}{2}\dbinom{2}{0}}{\dbinom{2+2+2}{2}}=1-\dfrac{6(1)}{15}$$

$$=\dfrac{3}{5}$$