Higher November 2018 Paper 2 Q12

12. Jenny is setting up a stall offering prizes in a community hall.
She has a bag of white, red, green and black balls.
All the balls in the bag are the same size.

A player pays £1 to select a ball at random.
The probability that a player selects:

• a white ball is 0·4,
• a red ball is 0·2,
• a green ball is 3 times the probability of selecting a black ball.

When either a black ball or a red ball is selected the player will win a prize.
The prizes are:

• £2.50 for selecting a black ball,
• £1.50 for selecting a red ball.

Any ball selected is to be placed back into the bag before the next player has a go.

If 300 players select a ball, show that Jenny can expect to make a profit in excess of £125. [4]