If you flipped a penny and a nickel, and rolled a die, what is the probability of:

a. getting at least one head on the coins and a 6 on the die?

b. getting a head on both coins and a 4 on the die ?

c. getting a head on both coins and a 3 or a 5 on the die?

d. getting a head on both coins with anything on the die?

A. 1/12

b. 1/24
c. 1/12
d. 1/4

I THINK these answers are correct, if this is for a major grade, ask somebody and compare my answers to theirs.

Another person had the exact same answers as you. This is for a major grade! Thank You!!

. P(at least one head) is the same as 1 - P(no heads). Now, P(no heads) = 1/2 * 1/2 = 1/4 so P(at least one head) = 3/4. P(6) = 1/6. The total is 3/4 * 1/6 = 1/8.

actually for part a is it possible the answer could be 1/8?

Yes, the answer to (a) is 3/4 x 1/6 = 1/8

3/4 is the probability of getting at least one head in two coin tosses.

To calculate the probabilities for these scenarios, we need to understand the concept of probability and use some basic principles of probability. The probability of an event happening is the number of favorable outcomes divided by the total number of possible outcomes.

a. To calculate the probability of getting at least one head on the coins and a 6 on the die, we need to consider the possible outcomes:

Coins: H (head) or T (tail)
Die: 1, 2, 3, 4, 5, or 6

Since we want at least one head on the coins, the favorable outcomes are either H-T, T-H, or H-H. And we want a 6 on the die, which is one favorable outcome. So the total number of favorable outcomes is 3 (H-T, T-H, H-H) x 1 (6 on die) = 3.

The total number of possible outcomes is 2 (coins) x 6 (die) = 12.

Therefore, the probability of getting at least one head on the coins and a 6 on the die is 3/12, which simplifies to 1/4 or 25%.

b. To calculate the probability of getting a head on both coins and a 4 on the die, we need to consider the possible outcomes:

Coins: H (head) or T (tail)
Die: 1, 2, 3, 4, 5, or 6

Since we want a head on both coins, the favorable outcome is H-H. And we want a 4 on the die, which is one favorable outcome. So the total number of favorable outcomes is 1 (H-H) x 1 (4 on die) = 1.

The total number of possible outcomes is 2 (coins) x 6 (die) = 12.

Therefore, the probability of getting a head on both coins and a 4 on the die is 1/12.

c. To calculate the probability of getting a head on both coins and a 3 or a 5 on the die, we need to consider the possible outcomes:

Coins: H (head) or T (tail)
Die: 1, 2, 3, 4, 5, or 6

Since we want a head on both coins, the favorable outcome is H-H. And we want a 3 or a 5 on the die, which are two favorable outcomes. So the total number of favorable outcomes is 1 (H-H) x 2 (3 or 5 on die) = 2.

The total number of possible outcomes is 2 (coins) x 6 (die) = 12.

Therefore, the probability of getting a head on both coins and a 3 or a 5 on the die is 2/12, which simplifies to 1/6 or approximately 16.67%.

d. To calculate the probability of getting a head on both coins with anything on the die, we need to consider the possible outcomes:

Coins: H (head) or T (tail)
Die: 1, 2, 3, 4, 5, or 6

Since we want a head on both coins, the favorable outcome is H-H. And we want anything on the die, which is six favorable outcomes. So the total number of favorable outcomes is 1 (H-H) x 6 (die outcomes) = 6.

The total number of possible outcomes is 2 (coins) x 6 (die) = 12.

Therefore, the probability of getting a head on both coins with anything on the die is 6/12, which simplifies to 1/2 or 50%.