The six sides of a number cube are labeled 1, 2, 3, 4, 5 and 6. You flip a coin and roll the number cube.

Question

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The six sides of a number cube are labeled 1, 2, 3, 4, 5 and 6. You flip a coin and roll the number cube. What is the theoretical probability that the coin lands on tails and you roll a number less than 3? Write your answer as a fraction.

Answer 1

Explanation:

In general, probability is determined by this ratio:

(number of ways it could happen)/( total number of outcomes)

There are going to be two ratios, since there are two questions, do them one at a time:

NUMBER CUBE:

Number of ways it could happen: 2 (there are only 2 faces on the die less than 3, so only two ways it could happen)

Number of total outcomes: 6 (there are 6 total faces on the die, therefore 6 possible outcomes)

Ratio: 2/6 =1/3

COIN:

Number of ways it could happen: 1 (there is only one side of "tails" on a coin)

Number of total outcomes: 2 (there are two sides of a coin)

Ratio: 1/2



TAKING THEM TOGETHER:

Since these are independent events, we multiply the results of each event. Therefore the probability of rolling less than 3 and flipping tales is:

1/2 x 1/3 = 1/6