Question

Which event has exactly 12 possible outcomes?

Answer 1

Answer:

rolling a number cube with sides labeled 1 through 6 and tossing a coin.

Step-by-step explanation:

We will resolve each statement to determine the events that has exactly 12 possible outcomes.

N = number of possible outcomes for a cube

Nc = number of possible outcomes for a coin

Nca = number of possible outcomes for the cards

i. rolling a number cube with sides labeled 1 through 6 and then rolling the number cube again

Nt = N × N

N = 6 ( cube has 6 possible outcomes and its rolled twice)

Nt = 6 × 6 = 36

ii. tossing a coin and randomly choosing one of 4 different cards.

Nt = Nc × Nca

Nc = 2 ( coin has two outcomes)

Nca = 4 ( 4 possible cards )

B = 2 × 4 = 8

iii. rolling a number cube with sides labeled 1 through 6 and tossing a coin.

N = N × Nc

N = 6 ( cube has 6 possible outcomes)

Nc = 2 (coin has two faces)

N = 6 × 2 = 12 (correct)

Iv. tossing a coin 6 times.

N = Nc^6

Nc = 2

N = 2^6 = 64

Therefore, the correct answer is iii.

rolling a number cube with sides labeled 1 through 6 and tossing a coin.