Two tickets are drawn without replacement from the following

Two tickets are drawn without replacement from the following box of tickets: express all of your answers accurate to four decimal places. Find probability that the first ticket is an even number. Find probability that second ticket is an odd number given that the first ticket was 7. probability that second ticket is an odd number.

Solution

1.

There are 7 tickets with 3 even numbered tickets.

SO probability of first ticket being even number is :3/7

2.

If first ticket was 7 and we are choosing without replacement so we have 6 tickets left numbered from 1 to 6. SO 3 odd and 3 even tickets.

So probabiity of second ticket being odd number given first ticket being 7 is:3/6=1/2

3.

Two mutually exclusive cases:

1. First ticket is even number.

Probability of this is:3/7

So there are 6 tickets left with 4 odd and 2 even to choose an odd number from

So probability is, p=4/6*3/7=12/42

2. First ticket is odd number. Probability of this is:4/7

So there are 6 ticket lef tiwht 3 odd and 3 even to choose odd number from

So probability is, q=3/6*4/7=12/42

So total probability of choosing odd number is:12/42+12/42=24/42=4/7