Question

Jose rolls the number cube and then spins the spinner. What is the probability that he rolls a number less than 3 and then spins a number less than 3?

Answer 1

1. 48

2. 16

3. 12

Explanation:

Here are some basic facts:

p(outcome) = (number of desired outcomes)/(total number of possible outcomes)

p(two independent events) = p(event 1) × p(event 2)

The spinner and cube are independent of each other. Therefore, the combined probabilitiy of a certain spin followed by a certain roll is the product of the two separate probabilities.

Spinner: total number of possible outcomes = 8

Cube: total number of possible outcomes = 6

1.

Spin a 5. Roll a 6.

Desired outcome of spinner: 5

Number desired outcomes of spinner: 1

desired outcome of cube: 6

Number of desired outcomes of the cube: 1

p(spin a 5 and roll a 6) = 1/8 × 1/6 = 1/48

2.

Spin an odd number. Spin a 3.

Desired outcomes of spinner: odd number, 1, 3, 5, 7

Number desired outcome of spinner on first spin: 4

Desired outcomes of spinner: 3

Number of desired outcomes of spinner on second spin: 1

p(spin an odd number and then spin a 3) = 4/8 × 1/8 = 4/64 = 1/16

1.

Roll less than 3. Spin less than 3.

Desired outcomes of the cube: less than three, 1, 2

Number desired outcome of cube: 2

Desired outcomes of spinner: less than three, 1, 2

Number of desired outcomes of spinner: 2

p(roll less than 3 and spin less than 3) = 2/6 × 2/8 = 4/48 = 1/12