GSCE MathematicsProblem Solving

Handling DataHigher Tier

Katy likes coffee.

Sometimes she takes it without milk or sugar, sometimes she has either milk or sugar, but prefers to take it with milk and sugar.

The probability that she has a cup of coffee without milk or sugar is 0·1, and the probability that she has it with both is 0·6.

She is five times more likely to have a cup of coffee with only milk than she is to have it with only sugar.Calculate the probability that she has a cup of coffee with milk only.

Helping handYou may want to draw a tree diagram or a Venn diagram to help you.Fill in the information you know, then find out the probability of either having just milk or just sugar.Think carefully about the ratio of milk:sugar

AnswerM

NM

S

S

NS

NS

P( Milk & Sugar) = 0.6

1 – 0.6 – 0.1 = 0.3

So P(just milk OR just sugar) = 0.3

Remember: Total

probability = 1

P( No Milk & No Sugar) = 0.1

Katy is 5 times more likely to have coffee with just milk than she is to have it with only sugar. M : Si.e. 6 parts 0.3 = 0.05 5 : 1

6

So just milk – 5 parts: 5 x 0.05 = 0.25

Or/

M S

0.6

0.1

So 1 – 0.6 – 0.1 = 0.3

P(just milk OR just sugar) = 0.3

Katy is 5 times more likely to have coffee with just milk than she is to have it with only sugar.

M : S

i.e. 6 parts 0.3 = 0.05 5 : 1

6

So just milk – 5 parts: 5 x 0.05 = 0.25

Remember: Total

probability = 1