# 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? 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...

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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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