Answer:
a) The probability that the player wins is 2/5 or 0.4
b) Yes, the probability changes if the two numbers are multiplied
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