A box contains five slips of paper. Each slip has one of the number 4, 6, 7, 8, or 9 written on it and all numbers are used. The first player reaches into the box and draws two slips and adds the two numbers. If the sum is even, the player wins. If the sum is odd, the player loses.

a. What is the probability that the player wins?

b. Does the probability change if the two numbers are multiplied? Explain.

a) The probability that the player wins is 2/5 or 0.4

b) Yes, the probability changes if the two numbers are multiplied

Step-by-step explanation:

* Lets explain how to solve the problem

- There are five slips each one has one number 4, 6, 7, 8, 9

- All numbers are used

- The first player reaches into the box and draws two slips and adds

the two numbers

- If the sum is even, the player wins

- If the sum is odd, the player loses

* To find the probability of win we must to find all the even sum

∵ The player will chose two slips

∴ There are 5 choices of the 1st number and 4 choices for the

2nd number

∴ The total choices for the two numbers = 5 * 4 = 20

a)

- Lets find the sum of the two numbers

# The first number is 4

∵ 4 + 6 = 10, 4 + 7 = 11, 4 + 8 = 12, 4 + 9 = 13

∴ There are 2 even sum

# The first number is 6

∵ 6 + 4 = 10, 6 + 7 = 13, 6 + 8 = 14, 6 + 9 = 15

∴ There are 2 even sum

# The first number is 7

∵ 7 + 4 = 11, 7 + 6 = 13, 7 + 8 = 15, 7 + 9 = 16

∴ There are 1 even sum

# The first number is 8

∵ 8 + 4 = 12, 8 + 6 = 14, 8 + 7 = 15, 8 + 9 = 17

∴ There are 2 even sum

# The first number is 9

∵ 9 + 4 = 13, 9 + 6 = 15, 9 + 7 = 16, 9 + 8 = 17

∴ There are 1 even sum

∴ The total of even sum = 2 + 2 + 1 + 2 + 1 = 8 even sum

- Probability = the number of ways of success : the total number of

possible outcomes

∵ The number of even sum = 8

∵ The total outcomes = 20

∴ P (even sum) = 8/20 = 2/5

* The probability that the player wins is 2/5 or 0.4

b)

- Lets find the product of the two numbers

# The first number is 4

∵ 4 * 6 = 24, 4 * 7 = 28, 4 * 8 = 32, 4 * 9 = 36

∴ There are 4 even product

# The first number is 6

∵ 6 * 4 = 24, 6 * 7 = 42, 6 * 8 = 48, 6 * 9 = 54

∴ There are 4 even product

# The first number is 7

∵ 7 * 4 = 28, 7 * 6 = 42, 7 * 8 = 56, 7 * 9 = 63

∴ There are 3 even product

# The first number is 8

∵ 8 * 4 = 32, 8 * 6 = 48, 8 * 7 = 56, 8 * 9 = 72

∴ There are 4 even product

# The first number is 9

∵ 9 * 4 = 36, 9 * 6 = 54, 9 * 7 = 63, 9 * 8 = 72

∴ There are 3 even product

- Lets find the probability of the even product

∴ The total of even product = 4 + 4 + 3 + 4 + 3 = 18 even product

∵ The number of even product = 18

∵ The total outcomes = 20

∴ P (even sum) = 18/20 = 9/10

∴ The probability that the player wins is 9/10 or 0.9

* Yes, the probability changes if the two numbers are multiplied