**Dr Chris Luke, AC for Northamptonshire and Rutland**

1) I have a £1 coin and a £2 coin, which are both fair. Without showing you, I flip both coins. Then I tell you that the £2 coin landed heads. What is the probability that the £1 coin landed tails?

2) I have two indistinguishable £1 coins, which are both fair. Without showing you, I flip both coins. Then I tell you that one of the coins landed heads. What is the probability that the other coin landed tails?

3) Mrs Smith is a woman you know nothing about apart from the following two facts: Mrs Smith has two children; and her oldest child is a girl. What is the probability that Mrs Smith has a son?

4) Mrs Patel is a woman you know nothing about apart from the following two facts: Mrs Patel has two children; and she has a daughter. What is the probability that Mrs Patel has a son?

No cheating! When you’re done, view the answers here.