Question

A game consists of randomly choosing a bag (labelled 1, 2 or 3) out of a choice of 100, and then again randomly, picking a ball (red or black) from it. Each bag has the same total number of balls (10)

a) complete the tree diagram
b) Work out the probability that a player will select a red ball
c) the same player is going to play the game 200 times consecutively. How many black balls should he expect to pick?

Answer 1

There is no partial sketch of the tree to be completed.

A complete version of the tree sketch is attached. See picture below

Answer:

A.) See attached picture

B.) 0.44

C.) 112

Explanation:

B.) The probability that a player selects a red ball:

[ (0.35*0.6) + (0.45*0.2) + (0.2*0.7) ]

0.21 + 0.09 + 0.14 = 0.44

C.) the same player is going to play the game 200 times consecutively. How many black balls should he expect to pick?

The probability that a player selects a black ball = 1 - probability of selecting a red ball

1 - 0.44 = 0.56

0.56 * 200 = 112