# A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the pro

Discussion in 'Calculator Requests' started by math_celebrity, Dec 8, 2019.

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A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form

Let's review the vitals of this question:
• The probability of heads on a fair coin is 1/2.
• On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability.
• So we have a combination of outcomes below:
Outcomes
For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities:
1. P(Heads and 4) = 1/2 * 1/6 = 1/12
2. P(Heads and 5) = 1/2 * 1/6 = 1/12
3. P(Heads and 6) = 1/2 * 1/6 = 1/12

Since we want any of those events, we add all three probabilities
1/12 + 1/12 + 1/12 = 3/12

This fraction is not simplified. So we type this fraction into our search engine, and choose Simplify.

We get a probability of 1/4.

By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine:
1/4 to decimal