After weeks of begging from her children Emma has given in and agreed to put the Christmas decorations up at the weekend.
Emma has been in the loft to sort out the decorations.
One of the boxes has 15 baubles in it.
10 of the baubles are gold and 5 are red.
Emma’s daughter Freya picks two baubles at random from the box.
Work out the probability that Freya picks one of each colour of bauble.
Answer:
Probability that 1st decoration is red = 5/15
Probability that 1st decoration is gold = 10/15
Probability that 2nd decoration is red given 1st was gold = 5/14
Probability that 2nd decoration is gold given 1st was red = 10/14
If we need the probability that one decoration is red and the other gold, the combinations are:
1st decoration was gold and 2nd was red
1st decoration was red and 2nd was gold
Probability that one decoration is gold and the other red = (5/15 x 10/14) + (10/15 x 5/14) = 100/210 = 10/21