The standard deck of cards has 52 cards: 13 cards in 4 suits.

Ways to choose three hearts:  13 * 12 * 11 = 1716

Ways to choose three cards:  52 * 51 * 50 = 132600

Probability is a number between 0 and 1 that is defines as the total ways of what you want ÷ by the total ways

The resulting simplified fraction is 11/850

In the set of 1 to 15, two numbers, 6 and 12, are multiples of 6. That means there are two chances out of 15 to select a multiple of 6.

2/15

To solve the problem one must calculate that there are 50 orange crayons in the box. So ⁵⁰/₁₂₀ are orange. If we simplify that fraction by 10 we get 5/12.

Find the area of the entire field and the target area. The fraction of the field that is the target area is equal to the probability of the skydiver hitting the target area. For example, if the field were 100 m³ and the target area was 100 m³ than the probability would be 1. If the field were 100 m³ and the target area was 50 m³ than the probability would be 0.5 and so on.

(50 * 50)/(1000 * 500) = 5/1000 = 1/200

You take the probability of the first outcome times the probability of the second, so (2/9) * (1/8) = 2/72 = 1/36

First, let's consider all of the pairs that could be chosen from R and Q. There are sixteen possibilities:

1 and 2; 1 and 6; 1 and 8; 1 and 24; 3 and 2; 3 and 6; 3 and 8; 3 and 24; 4 and 2; 4 and 6; 4 and 8; 4 and 24; 12 and 2; 12 and 6; 12 and 8; 12 and 24.

Now, we need to find the product of each of these pairs, and then determine whether or not they belong to Q. The products of all of the possible pairs would be as follows:

1(2) = 2, which belongs to Q

1(6) = 6, which belongs to Q

1(8) = 8, which belongs to Q

1(24) = 24, which belongs to Q

3(2) = 6, which belongs to Q

3(6) = 18, which doesn't belong to Q

3(8) = 24, which belongs to Q

3(24) = 72, which doesn't belong

4(2) = 8, which belongs to Q

4(6) = 24, which belongs to Q

4(8) = 32, which doesn't belong

4(24) = 96, which doesn't belong

12(2) = 24, which belongs to Q

12(6) = 72, which doesn't belong

12(8) = 96, which doesn't belong

12(24) = 288, which doesn't belong

Thus, of our sixteen possible combinations, there are 9 which, when multiplied, give a number that belongs to Q. Because probability is the number of successful events out of the total number of events, the probability is 9/16.

The answer is 9/16.

Only John's statement must be true. Suzy could have freckles and not be Tim's sibling and if Jake doesn't have freckles then he is not Tim's sibling.

The probability that a blue marble is chosen first is 5/10 because at the outset there are 5 blue marbles in a total of 10 marbles.  After one marble has been chosen, there are 9 total marbles remaining since there is no replacement.  The probability that a red marble is chosen in the second pick is 3/9 (because there are 3 red marbles out of a total of 9).  There are now 8 total marbles remaining and 2 green marbles. Thus, the probability of picking a green marble on the third pick is 2/8. 

Therefore, the probability of picking a blue-red-green marble outcome (in that order) is:

5/10 * 3/9 * 2/8 = 30/720 = 1/24

Thinking through our data, we know that we are looking for the following combination of events, where T is a theology book, and < > represents a draw from the shelf:

1. <T><T>

2. <T><Non-T>

3. <Non-T><T>

To save us quite a bit of trouble, let us note that only one event is excluded:

<Non-T><Non-T> 

The easiest way to solve this would be to solve for the probability of this one case and subtract that from 1. This will give us the "remaining probability" that applies to the three cases that we want.

The <Non-T><Non-T> case would be calculated:

First draw: 25/40 = 5/8

Second draw: 24/39 = 8/13

Total probability: (5/8) * (8/13) = 5/13

The probability of our case is 1 – (5/13) = (13 – 5)/13 = 8/13.