Probability is the likelihood, expressed as a number between 0 and 1, that a certain event will occur. The number can be represented as a ratio or fraction, a decimal, as well a percentage. For example a 25% chance of an event occurring can be also be stated as a 1out of 4 chance or a 0.25 chance.
Since we can not know for certain what exact outcomes will be, we can express the likeliness of the outcome as probability.
There are two basic approaches to probability, experimental probability and theoretical probability. Experimental probability is found by repeating an experiment and observing the outcomes. The possible outcomes within an experiment is the called the sample space.
Theoretical probability is found by using the possible number of desired outcomes when an even does occur.
Below shows the event of flipping a coin with both approaches. If you need more review select the video links provided.
Since we can not know for certain what exact outcomes will be, we can express the likeliness of the outcome as probability.
There are two basic approaches to probability, experimental probability and theoretical probability. Experimental probability is found by repeating an experiment and observing the outcomes. The possible outcomes within an experiment is the called the sample space.
Theoretical probability is found by using the possible number of desired outcomes when an even does occur.
Below shows the event of flipping a coin with both approaches. If you need more review select the video links provided.
Review of Basic Experimental/Theoretical ProbabilityExperimental and theoretical probability is a review from previous math courses but it is important to review the concept in order to build on it.
Select the Khan Academy review links for a review. Remember to use the hints or videos when needed. |
Comparing ProbabilitiesSince probability can be expressed as a fraction/ratio, decimal or percentage you will need to review the conversions. In the Khan Academy practice exercise you will be comparing probabilities written in different forms. Converting into a percentage can be the easiest way of comparing probabilities. If you need to review how to convert between decimals, fractions, and percentages select the button below for a review chart.
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Independent and Dependent Events
When a single event occurs there are no additional influences that will affect the probability of a specific outcome. However when combined events (or multiple events) occur, they may or may not affect each other. When flipping a coin 10 times the probably of landing on heads will not change from flip #1 to flip #2. It will always be a 50/50 chance. This is an example of an independent event. Independent events are when the occurrence of one event does not affect the probability of the other.
Lets say that you draw 2 cards from a set of playing cards. The probability of selecting a black card on the first draw is 26/52 or 50% since half of the deck is black. However if you select a 2nd card without replacing the first, the probability will now be different since you removed a card from the deck with the first draw. This is an example of a dependent event. Dependent events are when the occurrence of one event does affect the probability of the other.
Lets say that you draw 2 cards from a set of playing cards. The probability of selecting a black card on the first draw is 26/52 or 50% since half of the deck is black. However if you select a 2nd card without replacing the first, the probability will now be different since you removed a card from the deck with the first draw. This is an example of a dependent event. Dependent events are when the occurrence of one event does affect the probability of the other.
Calculating Independent and Dependent Events
Now lets calculate the probability of compound events using the Multiplication Rule of Probability. When finding the probability of compound independent events, you will need to start by finding the probability of each individual event. Since they do not affect each other, the same process is used from the theoretical and experimental probabilities from above. Once you find the probability of each occurring, you just need to multiply them together. See the example to in the chart to the left. After multiplying the two probabilities, you are given a 1 out of 25 chance of pulling 2 black marbles in a row if you put the first black marble back.
When calculating Dependent events, the same concept is used. However, since the probability of 2nd event depends on what happened in the 1st, this must be taken into consideration to find the individual probability of the 2nd event. Notice in the example to the right, the probability of the 2nd marble being black after you choose the first black marble goes from a 2/10 chance to a 1/9 chance. Therefore there is a 1 out of 45 chance of pulling 2 black marbles when you keep the 1st.
When calculating Dependent events, the same concept is used. However, since the probability of 2nd event depends on what happened in the 1st, this must be taken into consideration to find the individual probability of the 2nd event. Notice in the example to the right, the probability of the 2nd marble being black after you choose the first black marble goes from a 2/10 chance to a 1/9 chance. Therefore there is a 1 out of 45 chance of pulling 2 black marbles when you keep the 1st.
Complete the worksheet that is attached below, then check your answers.
Complete the Khan Academy Practice assignments below. Take them as many times as you need to be proficient.