BASIC PROBABILITY PROBLEMS

Concept: Probability, chance, and odds are different ways of expressing the likelihood that an event will occur.

Probability is the likelihood that a particular event will occur. Probability is written as a ratio. Probability is the ratio of the number of favorable outcomes to the number of possible outcomes

Chance is a way of expressing the likelihood of an event. It is the probability of an event expressed as a percent. We can use the word chance and a percent to describe a probability. If a probability is expressed as ¼, we can say that the chance of that thing happening is 25 percent.

Percent chance of a probability of ¼ = 1 4 = 0.25 = 25%

Odds is the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

Note that odds are usually expressed by using the word “to”, or when writing the expression mathematically by using a colon, not by using a division line. Odds are reduced just as are other ratios.

odds = number of favorable outcomes TO number of unfavorable outcomes.

or written mathematically

X : Y

( When X = number of favorable outcomes, and Y = number of unfavorable outcomes )

Unfavorable outcomes can be calculated by subtracting the favorable outcomes from the possible outcomes.

Calculation for Unfavorable Outcomes

possible outcomes - favorable outcomes. unfavorable outcomes

Steps for Solving Basic Probability Problems

Step 1 | Determine what kind of question you are being asked. Are you being asked to find a probability fraction, a chance (percent probability), or the odds?
Step 2 | If you are being asked to find a probability fraction, set up the probability fraction. Reduce as necessary.
Step 3 | If you are being asked to find a percent probability, set up the probability fraction as defined in Step 2. Reduce as necessary. Solve the division. Convert the decimal answer to a percent.
Step 4 | If you are being asked to find the odds, first set up a probability fraction. Reduce as necessary. Set up the ratio of favorable outcomes to unfavorable outcomes.
Step 5 | Write your final answer.

Example 1: There are 13 socks in a bag. If there is one yellow sock and 9 white socks, what is the probability fraction of drawing a yellow sock from the bag?

Step 1 | Determine what kind of question you are being asked. Are you being asked to find a probability fraction, a chance (percent probability), or the odds? | probability fraction
Step 2 | If you are being asked to find a probability fraction, set up the probability fraction. | 1 13
| Reduce as necessary. | No reduction necessary.
Step 3 | If you are being asked to find a percent probability, set up the probability fraction as defined in Step 2. Reduce as necessary. Solve the division. Convert the decimal answer to a percent. | Does not apply.
Step 4 | If you are being asked to find the odds, first set up a probability fraction. Reduce as necessary. Set up the ratio of favorable outcomes to unfavorable outcomes. | Does not apply.
Step 5 | Write your final answer. | 1 13

Example 2: There are 11 socks in a bag. If there are 11 blue socks, what is the percent probability of drawing a blue sock from the bag (to the nearest hundredth)?

Step 1 | Determine what kind of question you are being asked. Are you being asked to find a probability fraction, a chance (percent probability), or the odds? | chance (percent probability)
Step 2 | If you are being asked to find a probability fraction, set up the probability fraction. Reduce as necessary. | Does not apply.
Step 3 | If you are being asked to find a percent probability, set up the probability fraction as defined in Step 2. | 11 11
| Reduce as necessary. | No reduction necessary.
| Solve the division. |
| Convert the decimal answer to a percent. | 1.0 = 100%
Step 4 | If you are being asked to find the odds, first set up a probability fraction. Reduce as necessary. Set up the ratio of favorable outcomes to unfavorable outcomes. | Does not apply.
Step 5 | Write your final answer. | 100%

Example 3: There are 9 M&Ms in a suitcase. If there is 1 white M&M, what are the odds of drawing a white M&M from the suitcase?

Step 1 | Determine what kind of question you are being asked. Are you being asked to find a probability fraction, a chance (percent probability), or the odds? | odds
Step 2 | If you are being asked to find a probability fraction, set up the probability fraction. Reduce as necessary. | Does not apply.
Step 3 | If you are being asked to find a percent probability, set up the probability fraction as defined in Step 2. Reduce as necessary. Solve the division. Convert the decimal answer to a percent. | Does not apply.
Step 4 | If you are being asked to find the odds, first set up a probability fraction. | 1 9
| Reduce as necessary. | Not necessary
| Set up the ratio of favorable outcomes to unfavorable outcomes. | 1 : (9-1) 1 : 8
Step 5 | Write your final answer. | 1 : 8