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College Algebra: Help and Review27 chapters | 230 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Jennifer Beddoe*

Determining the probability of compound events involves finding the probability of each event and then determining how to combine them. This lesson will give you the tools to find the probability and finish with a quiz to cement your knowledge.

A **compound event** is one in which there is more than one possible outcome. Determining the probability of a compound event involves finding the sum of the probabilities of the individual events and, if necessary, removing any overlapping probabilities.

Probability is the likelihood that an event will occur. It is written as a fraction with the number of favorable outcomes as the numerator and the total number of outcomes as the denominator. Favorable just means that a particular outcome is what you are curious about, not that it is necessarily positive.

Probability can be used to determine many things, from the likelihood that you will win the jackpot in the lottery to the likelihood that a baby will be born with a certain birth defect and anything in between. Probability is used extensively in the sciences, investing, weather reporting and many other areas.

Let's take a look at some examples.

1) What is the probability that you will roll a five using a 6-sided die?

The favorable outcome is rolling a five, and that can only occur once using one die. The total number of outcomes is six, since the die is 6-sided.

So the probability of rolling a five is 1/6.

2) What is the probability that you will pull a heart out of a standard deck of cards?

The favorable outcome would be pulling a heart and there are 13 of them in a standard deck. The total number of outcomes is 52 because there are 52 cards in a standard deck.

The probability of pulling a heart is 13/52 or 1/4.

A compound event is an event with two or more favorable outcomes. There are two types of compound events and determining the probability for each is different. First, let's talk about an exclusive compound event.

An **exclusive compound** event in one in which the multiple events do not overlap. The method for determining the probability of this type of compound event is to add together the probabilities of each event. The sum is the probability of the compound event. In mathematical terms - P(C) = P(A) + P(B)

Let's take a look at some examples:

1) What is the probability of rolling either a two or a four using one 10-sided die?

The probability of rolling a two is 1/10 and the probability of rolling a four is 1/10. So, the compound probability is:

P(C) = 1/10 + 1/10 = 2/10 or 1/5

2) What is the probability of pulling any face card or a three of clubs from a standard deck of cards?

The probability of getting a face card is 12/52 and the probability of getting a three of clubs is 1/52, so the compound probability is:

P(C) = 12/52 + 1/52 = 13/52 or 1/4

An **inclusive compound** event is one in which there is overlap between the multiple events. Problems like rolling a two or an even number are inclusive because two is an even number. The probability of pulling a club or a face card from a deck of cards is also inclusive because three of the face cards will be clubs.

The formula for determining the probability of an inclusive compound event is:

P(C) = P(A) + P(B) - P(A and B)

Because there is some overlap between the two events, the overlap needs to be subtracted out of the probability calculation; otherwise it will be counted twice and the probability will be higher than it should be.

Let's take a look at some examples:

1) What is the probability of rolling a prime number or a three using a 10-sided die?

The prime numbers between one and ten are two, three, five and seven, so the probability of rolling a prime number is 4/10.

The probability of rolling a three is 1/10

The overlap between the two probabilities is the three, so its probability (1/10) must be subtracted.

P(C) = 4/10 + 1/10 - 1/10 = 4/10 or 2/5

2) What is the probability of pulling a club or a face card from a standard deck of cards?

The probability of getting a club is 13/52.

The probability of getting a face card is 12/52.

The overlap would be those cards that are both clubs and face cards. There are three of them, so that probability is 3/52.

P(C) = 13/52 + 12/52 - 3/52 = 22/52 or 11/26.

A **compound event** is one in which there is more than one possible outcome. Determining the probability of a compound event involves finding the sum of the probabilities of the individual events and, if necessary, removing any overlapping probabilities. An **exclusive compound event** is one in which the multiple events do not overlap. In mathematical terms: P(C) = P(A) + P(B). An **inclusive compound event** is one in which there is overlap between the multiple events. The formula for determining the probability of an inclusive compound event is: P(C) = P(A) + P(B) - P(A and B).

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College Algebra: Help and Review27 chapters | 230 lessons | 1 flashcard set

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