Question

Aisha collects 1p coins and 2p coins. 24 of these are 1p coins. The probability of choosing a 2p coin at random is 1/2 How much money does she have in total?

Answer 1

Aisha has 24 2p coins and 24 1p coins, then she has in total:

2p*(24) + 1*p*(24) = 48p + 24p = 72p

Explanation:

Suppose that we have a set of N elements in a bag (if the bag is closed and we put our hand inside to grab one element, we could not distinguish them apart), and K of these elements have a given property (for example, these are red).

The probability of selecting at random one of these red elements is equal to the quotient between the number of elements with that property (K) and the total number of elements in the bag (N)

P = K/N

Now let's go to our problem.

We have 24 1p coins.

We have X 2p coins.

Then the total number of coins is: (24 + X)

We know that the probability of choosing at random a 2p coin is then:

P = X/(24 + X)

And we know that this is equal to 1/2

Then:

X/(24 + X) = 1/2

X = (1/2)*(24 + X) = 24/2 + X/2

X = 12 + X/2

X - X/2 = 12

X/2 = 12

X = 2*12 = 24

Then Aisha has 24 2p coins.

Aisha has 24 2p coins and 24 1p coins, then she has in total:

2p*(24) + 1*p*(24) = 48p + 24p = 72p