Design and Use a Simulation to Generate Frequencies for Compound Events: CCSS.Math.Content.7.SP.C.8c

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7th Grade Math › Design and Use a Simulation to Generate Frequencies for Compound Events: CCSS.Math.Content.7.SP.C.8c

Questions 1 - 10

A student flips a coin four times and rolls a six-sided die. What is the probability that the coin will land on heads all four times and the die will show a ?

$\frac{1}{96}$

$\frac{1}{16}$

$\frac{1}{6}$

$\frac{1}{22}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads four times in a row, we take the probability of the coin landing on heads and multiply it four times.

$\frac{1}{2}\times \frac{1}{2} \times\frac{1}{2}\times\frac{1}{2}=\frac{1}{16}$

Based on the question, we want to combine the probability of flipping a coin four times, with the coin landing on heads all four times, with the probability of rolling a on a die. There are sides to a die, and only one of those sides has the number ; thus, the probability of rolling a on a die is $\frac{1}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{16}\times\frac{1}{6}=\frac{1}{96}$

What is the probability of flipping a coin four times, with the coin landing on heads all three times, and rolling a , , or a on a die?

$\frac{1}{16}$

$\frac{1}{20}$

$\frac{1}{48}$

$\frac{1}{24}$

$\frac{1}{36}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads three times in a row, we take the probability of the coin landing on heads and multiply it three times.

$\frac{1}{2}\times \frac{1}{2} \times\frac{1}{2}=\frac{1}{8}$

Based on the question, we want to combine the probability of flipping a coin three times, with the coin landing on heads all three times, with the probability of rolling a , , or a on a die. There are sides to a die, and one of those sides has the number , one side has a , and one has the number ; thus, the probability of rolling a , , or a on a die is $\frac{3}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{8}\times\frac{3}{6}=\frac{3}{48}=\frac{1}{16}$

What is the probability of flipping a coin four times, with the coin landing on heads all four times, and rolling a or a on a die?

$\frac{1}{48}$

$\frac{1}{96}$

$\frac{1}{16}$

$\frac{1}{3}$

$\frac{1}{26}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads four times in a row, we take the probability of the coin landing on heads and multiply it four times.

$\frac{1}{2}\times \frac{1}{2} \times\frac{1}{2}\times\frac{1}{2}=\frac{1}{16}$

Based on the question, we want to combine the probability of flipping a coin four times, with the coin landing on heads all four times, with the probability of rolling a or a on a die. There are sides to a die, and one of those sides has the number and one has the number ; thus, the probability of rolling a or a on a die is $\frac{2}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{16}\times\frac{2}{6}=\frac{2}{96}=\frac{1}{48}$

What is the probability of flipping a coin three times, with the coin landing on heads all three times, and rolling a number on a die other than

$\frac{5}{48}$

$\frac{1}{20}$

$\frac{5}{6}$

$\frac{5}{57}$

$\frac{1}{48}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads three times in a row, we take the probability of the coin landing on heads and multiply it three times.

$\frac{1}{2}\times \frac{1}{2} \times\frac{1}{2}=\frac{1}{8}$

Based on the question, we want to combine the probability of flipping a coin three times, with the coin landing on heads all three times, with the probability of rolling any number on a die except . There are sides to a die, and five sides that aren't the number ; thus, the probability of rolling any number on a die except is $\frac{5}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{8}\times\frac{5}{6}=\frac{5}{48}$

What is the probability of flipping a coin two times, with the coin landing on heads all two times, and rolling any number on a die except ?

$\frac{5}{24}$

$\frac{1}{5}$

$\frac{1}{24}$

$\frac{5}{32}$

$\frac{1}{4}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads two times in a row, we take the probability of the coin landing on heads and multiply it two times.

$\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$

Based on the question, we want to combine the probability of flipping a coin two times, with the coin landing on heads all two times, with the probability of rolling any number on a die except . There are sides to a die, and five sides that aren't the number ; thus, the probability of rolling any number on a die except is $\frac{5}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{4}\times\frac{5}{6}=\frac{5}{24}$

What is the probability of flipping a coin four times, with the coin landing on heads all four times, and rolling a , , or a on a die?

$\frac{1}{32}$

$\frac{1}{30}$

$\frac{1}{16}$

$\frac{1}{20}$

$\frac{1}{24}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads four times in a row, we take the probability of the coin landing on heads and multiply it four times.

$\frac{1}{2}\times \frac{1}{2} \times\frac{1}{2}\times\frac{1}{2}=\frac{1}{16}$

Based on the question, we want to combine the probability of flipping a coin four times, with the coin landing on heads all four times, with the probability of rolling a , , or a on a die. There are sides to a die, and one of those sides has the number , one side has a , and one has the number ; thus, the probability of rolling a , , or a on a die is $\frac{3}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{16}\times\frac{3}{6}=\frac{3}{96}=\frac{1}{32}$

What is the probability of flipping a coin two times, with the coin landing on heads all two times, and rolling a , , or a on a die?

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{1}{16}$

$\frac{1}{24}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads two times in a row, we take the probability of the coin landing on heads and multiply it two times.

$\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$

Based on the question, we want to combine the probability of flipping a coin two times, with the coin landing on heads all two times, with the probability of rolling a , , or a on a die. There are sides to a die, and one of those sides has the number , one side has a , and one has the number ; thus, the probability of rolling a , , or a on a die is $\frac{3}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{4}\times\frac{3}{6}=\frac{3}{24}=\frac{1}{8}$

What is the probability of flipping a coin three times, with the coin landing on heads all three times, and rolling a on a die?

$\frac{1}{48}$

$\frac{1}{8}$

$\frac{1}{6}$

$\frac{1}{14}$

$\frac{1}{52}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads three times in a row, we take the probability of the coin landing on heads and multiply it three times.

$\frac{1}{2}\times \frac{1}{2} \times\frac{1}{2}=\frac{1}{8}$

Based on the question, we want to combine the probability of flipping a coin three times, with the coin landing on heads all three times, with the probability of rolling a on a die. There are sides to a die, and only one of those sides has the number ; thus, the probability of rolling a on a die is $\frac{1}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{8}\times\frac{1}{6}=\frac{1}{48}$

What is the probability of flipping a coin four times, with the coin landing on heads all four times, and rolling any number on a die except

$\frac{5}{96}$

$\frac{5}{6}$

$\frac{5}{16}$

$\frac{1}{32}$

$\frac{1}{96}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads four times in a row, we take the probability of the coin landing on heads and multiply it four times.

$\frac{1}{2}\times \frac{1}{2} \times\frac{1}{2}\times\frac{1}{2}=\frac{1}{16}$

Based on the question, we want to combine the probability of flipping a coin four times, with the coin landing on heads all four times, with the probability of rolling any number on a die except . There are sides to a die, and five sides that aren't the number ; thus, the probability of rolling any number on a die except is $\frac{5}{6}$

We want the probability of all of these events occurring, so we need to multiply:

$\frac{1}{16}\times\frac{5}{6}=\frac{5}{96}$

What is the probability of flipping a coin two times, with the coin landing on heads all two times, and rolling a or a on a die?

$\frac{1}{12}$

$\frac{1}{4}$

$\frac{2}{6}$

$\frac{1}{24}$

$\frac{1}{32}$

Explanation

There are two sides to a coin: heads and tails. The probability of the coin landing on heads is $\frac{1}{2}$

To determine the probability of the coin landing on heads two times in a row, we take the probability of the coin landing on heads and multiply it two times.

$\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$

Based on the question, we want to combine the probability of flipping a coin two times, with the coin landing on heads all two times, with the probability of rolling a or a on a die. There are sides to a die, and one of those sides has the number and one has the number ; thus, the probability of rolling a or a on a die is $\frac{2}{6}$