Question

A box contains 2 green and 3 white balls. A ball is selected at random from the box. If the ball is green, a card is drawn from a deck of 52 cards. If the ball is white, a card is drawn from the deck consisting of just the 16 pictures.
(a) What is the probability of drawing a king?
(b) What is the probability of a white ball was selected given that a king was drawn?

Answer 1

Answer:

a) $\frac{47}{260}$

b) $\frac{3}{20}$

Step-by-step explanation:

a) There are two ways of getting a king; picking a green ball and then picking a king from the deck of 52 OR picking a white ball then picking a king from the pictures only deck of 16

$P(king) = \frac{2}{5} *\frac{4}{52} +\frac{3}{5} *\frac{4}{16} = \frac{47}{260}$

b) $P(white ball, given king)= \frac{3}{5}*\frac{4}{16} =\frac{3}{20}$