Question

1. The number of typing errors on page follows a poisson distribution with a mean of 6.3. find the probability of having exactly six (6) errors on a page.

2. One bag contains 6 red, 2 blue, and 3 yellow balls. A second bag contains 2 red, 4 blue, and 5 yellow balls. A third bag contains 3 red, 7 blue, and 1 yellow ball. One bag is selected at random. If 1 ball is drawn from the selected bag, what is the probability that the ball drawn is yellow?

3. If one ball is drawn from 3 boxes, the first containing 3 red, 2 yellow, and 1 blue, the second box contains 2 red,2 yellow, and 2 blue, and the third box with 1 red, 4 yellow, and 3 blue. What is the probability that all 3 balls drawn are different colors?

Answer 1

1.

$$P(X=6)=\dfrac{e^{-6.3}(6.3)^6}{6!}=0.159461$$

2.

$$P(Y)=\dfrac{1}{3}(\dfrac{3}{6+2+3})+\dfrac{1}{3}(\dfrac{5}{2+4+5})$$

$$+\dfrac{1}{3}(\dfrac{1}{3+7+1})=\dfrac{3}{11}$$

3.

$$P(3\ different)=P(RYB)+P(RBY)$$

$$+P(YRB)+P(YBR)+P(BYR)+P(BRY)$$

$$=\dfrac{3}{6}(\dfrac{2}{6})(\dfrac{3}{8})+\dfrac{3}{6}(\dfrac{2}{6})(\dfrac{4}{8})+\dfrac{2}{6}(\dfrac{2}{6})(\dfrac{3}{8})$$

$$+\dfrac{2}{6}(\dfrac{2}{6})(\dfrac{1}{8})+\dfrac{1}{6}(\dfrac{2}{6})(\dfrac{1}{8})+\dfrac{1}{6}(\dfrac{2}{6})(\dfrac{4}{8})$$

$$=\dfrac{17}{72}$$