Question

A spinner is equally divided into three equal sectors and marked 2, 3, and 5. Five number cards are labeled 1, 1, 2, 3, and 4. Mike spins the spinner and draws a card randomly.

a) Use a possibility diagram to find the probability that Mike gets a zero when he subtracts the number on the spinner from the number on the card.
b)
Use a possibility diagram to find the probability that the product of the two resulting numbers is odd.
c)
What is the probability that the product of the two resulting numbers is at least 12

Answer 1

2/15 ; 6/15 ; 1/5

Explanation:

Number on spinner = (2, 3, 5)

Number on card = (1, 1, 2, 3, 4)

____ 2 ___ 3 ____ 5

1__1, 2 __ 1, 3 ___1, 5

1__1, 2 __ 1, 3 ___1, 5

2_ 2,2___2,3 ___2,5

3_ 3,2 __ 3,3 ___3,5

4_ 4,2 __ 4,3 ___4,5

1.)

To get a difference of 0:

{(2,2) ; (3,3)} = 2

Total possible outcomes = sample space = 15

P(difference of 0) = 2 / 15

2.)

Product of 2 resulting numbers is odd:

{(1,3) ; (1,5) ; (1,3) ; (1,5) ; (3,3) ; (3,5)} = 6

Total possible outcomes = 15

P(product is odd) = 6 /15

3.)

Product is atleast 12 :

{(3,5) ; (4,3) ; (4,5)} = 3

Total possible outcomes = 15

P(product is atleast 12) = 3/15 = 1/5