Kate and Nicola are selling raffle tickets at the summer fete.
In total 50 raffle tickets are sold.
The tickets sold are numbered from 1 to 50.
The raffle tickets are placed in a box for the draw.
One raffle ticket is selected at random and not replaced in the box.
A second ticket is then randomly selected.
Find the probability that one of the tickets drawn is odd and the other is even.
Answer:
Probability that 1st ticket is odd = 25/50 = ½
Probability that 1st ticket is even = 25/50 = ½
Probability that 2nd ticket is odd given 1st was even = 25/49
Probability that 2nd ticket is even given 1st was odd = 25/49
If we need the probability that one ticket is odd and the other even, the combinations are:
- 1st ticket was even and 2nd was odd
- 1st ticket was odd and 2nd was even
- Probability that one ticket is odd and the other even = (1/2 x 25/49) + (1/2 x 25/49) = 25/49