We have three choices for ice cream, three choices for sauces, and four choices for toppings.  Each selection is an independent event, so the choices are multiplied together: 3 * 3 * 4 = 36.

Probability is a number between 0 (will not happen) and 1 (will definitely happen).  Probability is generally a fraction where the numerator is the total of what you want to happen and the denominator is the total count.

Total ways to choose two red marbles:  3 * 2 = 6

Total ways to choose two marbles:  10 * 9 = 90

Therefore, the probability of choosing two red marbles is 6/90 or 1/15

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

Find the probabilty a junior's name will be pulled for a single lottery trial.  Then calculate the probability given 150 lottery trials.

(200 seniors * 2 entries each) + 300 juniors = 700 entries

For any single junior then, the odds are 1/700 for a single lottery trial.

For 150 trials, a junior will have (1/700 * 150 trials) = 150/700, which simplifies to

3/14 

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.