My wallet contains two 50p coins and five 20p coins only. I need 70p to buy an item. If I pick two coins at random from my wallet, what is the probability that I have picked the exact money to buy the item?

Answer:

8) C

We need exactly 70p worth of coins. So that is one 50p coin and one 20p coin. Best way to do this is to draw a tree diagram.

We can only take the dashed paths shown above.

1^st dashed path gives us = 2/7 x 5/6 = 10/42 = 5/21
2^nd dashed path gives us = 5/7 x 2/6 = 10/42 = 5/21

Total = 5/21 + 5/21 = 10/21

So the answer is C.