Denise rolls a number cube that has sides labeled 1 to 6 and then flips a coin.What Is the probability that she rolls an odd number and flips heads?

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We assume that the number cube and the coin are fair (e.g. the probabilities for each of the numbers on the cube is 1/6 and the probability of heads on the coin is 1/2.)

The probability of rolling an odd number on the cube is 1/2. (There are three outcomes in the event space: {1,3,5}, while the sample space has 6 items. The probability is the number of items in the event space divided by the number of items in the sample space or 3/6 which reduces to 1/2.

The probability of flipping heads is 1/2.

The probability of rolling an odd number and then flipping heads is (1/2)(1/2)=1/4 using the product principal.

The probability is 1/4 or .25

We could also list all of the possibilities: 1H  2H  3H  4H  5H  6H  1T  2T  3T  4T  5T  6T -- there are 12 items in the sample space. The event space is {1H,3H,5H}. Since there are 3 items in the event space, the probability is 3/12=1/4.

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