Bill and Ben each have three cards, numbered 4, 5 and 6.

4/5/6

456

Bill's cards

Ben's cards

They each take one of their own cards.

Then they add together the two numbers on the cards.

a) What is the probability that their answer is an odd number?

b) What is the probability that their answer is a number less than 11?

a) Probability = 4/9

b) Probability = 6/9

Step-by-step explanation:

Data Given:

Bill and Ben each have three cards 4,5 and 6. They each take one of their own cards. Then they add together the two numbers on the cards.

Find all the possibilities:

Bill = {4, 5, 6}

Ben = {4, 5, 6}

If both of them take one card, all possibilities are:

{ (4,4), (4,5), (4,6), (5,4), (5,5), (5,6), (6,4), (6,5), (6,6) }

Total No. of possibilities = 9

a) What is the probability that their answer is an odd number?

We see from the all possibilities listed above that which one of them has a sum of odd number. We get:

{ (4,5), (5,6), (5,6), (6,5) }

Total No. of Desired outcomes = 4

Total No. of possibilities = 9

Probability = Total No. of Desired outcomes/Total No. of possibilities

Probability = 4/9

b) What is the probability that their answer is a number less than 11?

We see from the all possibilities listed above that which one of them has a sum less than 11. We get:

{ (4,4), (4,5), (4,6), (5,4), (5,5), (6,4) }

Total No. of Desired outcomes = 6

Total No. of possibilities = 9

Probability = Total No. of Desired outcomes/Total No. of possibilities

Probability = 6/9