Working out probability :)

Question

Kia has 10 coins in a bag.

There are three £1 coins and seven 50 pence coins.

Kia takes at random, 3 coins from the bag.

Work out the probability that she takes exactly £2.50.

Thanks :)

Answer 1

One way to have the described event occur is to pick two £1 coins and one 50 p coin.

If only one coin valued at  £1 were picked, the remaining  £1.5 worth cannot be obtained by picking two 50p coins.

So it looks as if the only scenario satisfying the event described is as described in the first sentence above.

₃C₂ is # of ways of picking the two big value coins, and ₇C₁ is the # of ways of picking the coin of lesser value.

 

Therefore P(£2.50) = 3•7/₁₀C₃ ...I leave it to lyou to finish this calculation