Millie is at the village fete celebrating the May Day Bank Holiday with her family.
Millie’s Dad has bought her some sweets from one of the stalls.
Millie has 10 sweets in a bag.
5 are apple flavour sweets, 4 are strawberry flavour sweets and 1 is an orange sweet.
Millie chooses a sweet at random from the bag and eats it.
She then takes another sweet at random from the bag and eats it.
Find the probability that the two sweets Millie chooses have different flavours.
Answer:
If Millie picks an apple sweet first, then probability would be:
5/10 x 4/9 + 5/10 x 1/9 = 20/90 + 5/90 = 25/90
If Millie picks a strawberry flavour first, then probability would be:
4/10 x 5/9 + 4/10 x 1/9 = 20/90 + 4/90 = 24/90
If Millie picks an orange sweet first, then the probability would be:
1/10 x 5/9 + 1/10 x 4/9 = 5/90 + 4/90 = 9/90
So total probability = 25/90 + 24/90 + 9/90 = 58/90 = 29/45