If Rebecca rolls a pair of dice, the potential numbers that she could roll are below:

\(\displaystyle 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\)

Thus, there are 11 possible numbers that she could roll, of which 6 are even. 

Therefore, the probability of rolling an even number is \(\displaystyle \frac{6}{11}\).

If Alicia makes 1 out of 7 of the soccer goals that she attempts, this means that she makes \(\displaystyle \frac{1}{7}\) of her attempted soccer goals. 

If Alicia makes 49 soccer goal attempts, she will score on \(\displaystyle \frac{1}{7}\) of them. Given that \(\displaystyle \frac{1}{7}\) of 49 is 7, the correct answer is 7.

When a pair of dice is rolled, there are 11 possibilities. \(\displaystyle (2, 3, 5, 6, 7, 8. 9, 10, 11, 12)\)

The multiples of 4 are 4, 8, and 12. 

Therefore, the probability of rolling a multiple of 4 is \(\displaystyle \frac{3}{11}\).

Given that Virgo is a corgi, and that 1 in 5 corgis develop back problems, there is a 20 percent chance that Virgo will develop back problems. This is because 1 divided by 5 is .2, which is equivalent to 20 percent. 

To write probability as a fraction, put the number of things that match what you're looking for in the numerator and the total number of things in the denominator. In this case, what we're looking for is mugs. There are \(\displaystyle 3\) mugs, so we'll put \(\displaystyle 3\) in the numerator. The total number of things in the cupboard is \(\displaystyle 3\) mugs \(\displaystyle +4\) glasses \(\displaystyle +5\) cups. \(\displaystyle 3+4+5=12\), so we'll put \(\displaystyle 12\) in the denominator. This gives us \(\displaystyle \small \frac{3}{12}\), which we can simplify to \(\displaystyle \small \frac{1}{4}\). The correct answer is \(\displaystyle \small \frac{1}{4}\).

There are \(\displaystyle 6\) equally likely outcomes when rolling a die so each one of them has a probability of \(\displaystyle \frac{1}{6}\).  When you are finding the probability of a intersection, one event or another happening, you add the probabilities together.  So the probability of rolling a \(\displaystyle 1 (\frac{1}{6})\) plus the probability of rolling a \(\displaystyle 6 (\frac{1}{6})\) equals \(\displaystyle \frac{1}{3}\).

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

\(\displaystyle \text{Probability}=\frac{\text{Number of wanted outcomes}}{\text{Total number of outcomes}}\)

For this question, we do not want a red marble. This means that we are trying to find the proability of drawing either a blue or a green marble. Since we have \(\displaystyle 6\) blue marbles and \(\displaystyle 5\) green marbles, we have \(\displaystyle 11\) wanted outcomes. Since there is a total of \(\displaystyle 15\) marbles, we have a total of \(\displaystyle 15\) possible outcomes.

The probability then becomes the following:

\(\displaystyle \text{Probability}=\frac{11}{15}\)

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

\(\displaystyle \text{Probability}=\frac{\text{Number of wanted outcomes}}{\text{Total number of outcomes}}\)

First, write down the possible wanted outcomes:

\(\displaystyle 3, 6, 9\)

Now, because there are \(\displaystyle 3\) numbers divisible by three, we have \(\displaystyle 3\) wanted outcomes.

Since we are choosing numbers between \(\displaystyle 1\) and \(\displaystyle 10\), inclusive, we have a \(\displaystyle 10\) total outcomes.

The probability then can be written as the following:

\(\displaystyle \text{Probability}=\frac{3}{10}\)

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

\(\displaystyle \text{Probability}=\frac{\text{Number of wanted outcomes}}{\text{Total number of outcomes}}\)

First, write down the possible wanted outcomes:

\(\displaystyle 1, 2, 3\)

Now, because there are \(\displaystyle 3\) numbers that are less than \(\displaystyle 4\), we have \(\displaystyle 3\) wanted outcomes.

Since we are choosing numbers between \(\displaystyle 1\) and \(\displaystyle 10\), inclusive, we have a \(\displaystyle 10\) total outcomes.

The probability then can be written as the following:

\(\displaystyle \text{Probability}=\frac{3}{10}\)

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

\(\displaystyle \text{Probability}=\frac{\text{Number of wanted outcomes}}{\text{Total number of outcomes}}\)

First, write down the possible wanted outcomes. However, since all the numbers we are choosing from are negative, we have \(\displaystyle 0\) wanted outcomes.

Since we are choosing numbers between \(\displaystyle 1\) and \(\displaystyle 10\), inclusive, we have a \(\displaystyle 10\) total outcomes.

The probability then can be written as the following:

\(\displaystyle \text{Probability}=\frac{0}{10}=0\)