Question

Pita has 12 coins in her bag.
There are three £1 coins and nine 50p coins.

She takes 3 coins from the bag at random.

work out the probability that she takes exactly £2.50

Answer 1

Probability that she takes exactly £2.50 =  27/220

Number of coins in Pita's bag = 12

Number of £1 coins  =  3

Number of 50p coins  = 9

For Pita to take exactly £2.50 from the bag, it means she has to take two £1 coins and one 50p coin

Total number of coins that Pita has to take from the bag = 3

Number of ways of taking 3 coins out of 12 = 12C3

$12C3=\frac{12!}{(12-3)!3!}$

Number of ways of taking 3 coins out of 12 coins = 220 ways

Number of ways of taking two £1 coins from 3 £1 coins = 3C2

$3C2=\frac{3!}{(3-2)!2!}$

Number of ways of taking two £1 coins from 3 £1 coins = 3 ways

Number of ways of choosing one 50p coin from 9 50p coins = 9C1

$9C1 = \frac{9!}{(9-1)!1!}$

Number of ways of choosing one 50p coin from 9 50p coins = 9

Probability that she takes exactly £2.50 = (9x3)/220

Probability that she takes exactly £2.50 =  27/220

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