Find probability that the first ticket is an even number AND

Find probability that the first ticket is an even number AND the second ticket an odd number.

Solution

1) Probability that first ticket is an even number = (favourable outcomes)/(total outcomes) = (3)/(6) = 1/2

2) We need to find the probability that the second ticket is odd number given the first ticket was 7. If the first ticket was 7, then we have total outcomes = 5 and leftover odd outcomes = 2. Thereforefore, the required probability that the second ticket is odd given the first ticket was 7 = 2/5

3) Probability that the second ticket is an odd number = (1/2)(2/5)+(1/2)(3/5) = 2/10+3/10 = 5/10 = 1/2

4) Probability that the first ticket is an even number and second ticket is an odd number:

Since first ticket is an even number. Therefore, in the second draw, the total outcomes are 5 and favourable outcomes are 3. Hence, the required probability = 3/5