Using the Multiplication Rule In Exercises 19-32, use the Mult...

Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.

Accepted Answer

Welcome back, everyone. A jar contains 4 black pens and 6 blue pens. One pen is picked at random, and then a coin is flipped. What is the probability of picking a black pen and flipping a head? A 1/2, B 2/5, C 1/5, and D 17. So for this problem, let's define the two events of interest. First of all, we're picking a black pen. So let's find A as black pen. And B is flipping a hat, so we can just say hat. In this problem, we want to identify the probability of picking a black pen and flipping a hat. So that would be the probability of a intersection B. We have to understand that these events are independent because the outcome of A doesn't influence the outcome of B, right? Therefore, we're going to use the multiplication rule which says that we have to multiply the probability of A by the probability of B. So let's identify the probability of A. We have to take the number of favorable outcomes. We have a total of 4 black pens, so the number of favorable outcomes is 4, and divide that number by the total number of outcomes. We have 4 black and 6 blue pens, so the total number of outcomes is 4 + 6, which is 10. Meaning we're dividing 4 by 10, which gives us 0.4, or in a fraction form, 4 divided by 10 is the same as 2 divided by 5, right? We can divide both sides by 2. Now let's identify the probability of be occurring. What are the possible outcomes for a coin flip? We can have heads or sails, right? And we have equal probabilities for a fair coin, meaning the probability of be occurring is simply one half because we only have one favorable outcome that will be had and two possible outcomes, heads or tails. And now we can identify the probability of A and B occurring. That would be 2/5 multiplied by 1/2, which is equal to 2 divided by sum or 1 divided by 5. This corresponds to the answer to C. Thank you for watching.

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Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.

Key Concepts

Multiplication Rule of Probability

Independent Events

Calculating Probabilities

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Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.