Question

Manny rolls a number cube labeled 1 through 6 and spins a spinner with
four equal sections labeled 1, 2, 3, and 4. If both numbers are odd, he wins.
Otherwise, Gabriel wins. Usa a list to find the sample space. Then find the
probability that Gabriel wins.

Answer 1

The winning probability of Gabriel would be = 3/4.

Step-by-step explanation:

Given,

The sides of number cube = 6 {1, 2, 3, 4, 5, 6}

The sides of a spinner = 4  {1, 2, 3, 4}  

If both the gadgets are played together, the sample space (S) size would be:

6 x 4 = 24

Hence,

S = { (1, 1), (1, 2), (1, 3), (1, 4)  

       (2, 1), (2, 2), (2, 3), (2, 4)

       (3, 1), (3, 2), (3, 3), (3, 4)

       (4, 1), (4, 2), (4, 3), (4, 4)

       (5, 1), (5, 2), (5, 3), (5, 4)

       (6, 1), (6, 2), (6, 3), (6, 4) }

Manny wins if both the number are odd.

So, the winning chances of many are (1, 1), (1, 3), (3, 1), (3, 3) (5, 1) (5, 3) = 6

Therefore, the winning chances of Gabriel would be = 24 - 6 = 18

Therefore, the winning probability of Gabriel would be = 18/24 = 3/4.