Question

You are conducting an ’experiment’ where a 6-sided die is rolled (1, 2, 3, 4, 5, or 6), a coin is flipped (H, or T), and then you spin a wheel with 4 equally likely outcomes (a, b, c, or d).

Make the sample space of all possible outcomes?
State how many outcomes are possible (count up all possibe outcomes)?
What is the probability of getting a dice roll greater than 2, heads, and a or b on the spin?
What is the probability of getting tails or a none prime number dice roll?
What is the probability of getting a dice roll that is not 3 and a spin that is not a?
How many ways can you roll the die twice and spin the wheel three times? Is this a permutation or combination type of question?

Answer 1

The sample space for this experiment consists of all possible outcomes when a 6-sided die is rolled, a coin is flipped, and a wheel with 4 equally likely outcomes is spun. The probability of getting a dice roll greater than 2, heads, and a or b on the spin is 1/3. The probability of getting tails or a non-prime number dice roll is 3/4.

Step-by-step explanation:

The sample space for this experiment consists of all possible outcomes when a 6-sided die is rolled, a coin is flipped, and a wheel with 4 equally likely outcomes is spun. To find the sample space, we need to list all the possible outcomes:

{1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}

Counting the outcomes, we find that there are 12 possible outcomes.

To find the probability of getting a dice roll greater than 2, heads, and a or b on the spin, we need to count how many outcomes meet these conditions. The outcomes that satisfy these conditions are: {3H, 4H, 5H, 6H}. So, the probability is 4/12 or 1/3.

To find the probability of getting tails or a non-prime number dice roll, we need to count how many outcomes satisfy these conditions. The outcomes that satisfy these conditions are: {1T, 2H, 2T, 3T, 4H, 4T, 5H, 5T, 6T}. So, the probability is 9/12 or 3/4.

To find the probability of getting a dice roll that is not 3 and a spin that is not a, we need to count how many outcomes satisfy these conditions. The outcomes that satisfy these conditions are: {1H, 1T, 2H, 2T, 4H, 4T, 5H, 5T, 6H, 6T}. So, the probability is 10/12 or 5/6.

To find the number of ways you can roll the die twice and spin the wheel three times, we need to multiply the number of outcomes for each event. The number of outcomes for rolling the die twice is 36 (6 outcomes for the first roll and 6 outcomes for the second roll). The number of outcomes for spinning the wheel three times is 64 (4 outcomes for each spin). So, the total number of ways is 36 * 64 = 2304.

This is not a permutation or combination type of question. It is a question about the sample space, probability, and counting the number of outcomes.