Every result for a fair coin is independent of the previous trials.

The probability of landing heads or tails is .

For the coin to land on tails six consecutive times,

The answer is:  

To find the probability of an event, we will use the following formula:

Given the event of the teacher calling on a girl, we can calculate the following:

because there are 14 girl in the class.

We can also calculate the following:

because there are 26 total students in the class the teacher could potentially call on:

• 12 boys
• 14 girls

So, we substitute. We get

Therefore, the probability that the teacher calls on a girl is 

Start by figuring out the probability of rolling a  or . Since a six sided die has an equal chance of landing on each number, the probability would be , or .

Next, figure out the probability of spinning green. Since the spinner is divided equally into quarters, the probability of spinning green is .

Because the question asks about the probability of both events happening, you will need to multiply the two probabilities together.

Start by finding the probability of spinning an even number. We have  total possibilities for the spinner. Out of those six,  will give us even numbers: . Thus, we can write the following probability:

Next, determine the probability of rolling a  on the die. Since we are using a fair,  sided die, the probability of rolling a  will be .

Since the question asks about the probability of both events happening, we will need to multiply the two probabilities.

Recall the definition of a probability:

Now, the desired outcome for this scenario is the beanbag landing in the circle. Thus, we can use the area of the circle as the desired outcome. In addition, the total possible outcomes can then be represented by the area of the entire square playing field.

Start by finding the area of the playing field. Recall how to find the area of a square:

Plug in the given side length of the square.

Next, find the area of the circle.

Since the question informs us that the diameter of the circle is one-fourth that of the side of the square playing field, the diameter of the circle must be . It also follows that the radius of the circle must be .

Recall how to find the area of the circle.

Plug in the given radius to find the area of the circle.

Now that we have both areas, we can write probability:

Recall how to find the probability of an event:

Since there are  students out of the total  who have two pets, the probability for that occurring is .

Now, since we are selecting students without replacement, this means that the total number of students to choose from when it's time to select the second student is . There are also  students who have no pets, so we can write  as the probability that the second student selected will have no pets.

Since the question wants to know the probability of both events happening, we will multiply the probabilities together:

If you have a standard, six-sided die, what is the probability of rolling two numbers greater than 3 on two separate rolls?

We need to find the probability of two independent events. To do so, we need to find the probability of each event and multiply them.

There are three numbers on a six-sided die that are greater than 3 (4,5,and 6).

Thus, our probability of each event is

But, we want the probability of doing this twice, so we need to multiply our probabilities.

So, our answer is 

Each of the larger regions is one-eighth of the ring; each of the smaller regions is one-sixteenth of the ring. There are three small green regions and no large green regions, so the green portion of the ring is

of the ring. This is the probability that the arrow will land in a green region.

Recall what a probability is:

For the die, we can find the probability of rolling an even number:

Next, for the spinner, we can find the probability of landing on blue:

Since we want the probability of both evens happening, we will need to multiply the individual probabilities together:

Start by finding the individual probabilities of either event.

The probability of rolling a  is .

The probability of landing on either red or blue on the spinner is .

To find the probability of both events happening, you must multiply the two probabilities together.