Identifying the Complement
The probability of the complement of an event is always whatever probability it would take to reach 100%. If the probability of pulling a green marble out of a bag is 26%, then the probability of the compliment (pulling a not green marble) is 74%.
One benefit of viewing probabilities as decimals is that it is easy to calculate the complementary probability of a given event by subtracting the event probability (expressed as a decimal) from 1.
Finding the Complement
What is the complement to the event “Brian chooses one of the 2 red shirts from his drawer containing 10 shirts”?
The complement would be the other possibility: “Brian chooses one of the not red shirts from his drawer.”
1. If the probability of randomly choosing a Queen from a standard deck of 52 cards is .077, what is the probability of the complementary event?
The complement would be choosing a card that is not a Queen, and the complement probability would be the difference between .077 and 1:
Therefore, the if the probability of choosing a Queen is 7.7%, then the probability of choosing a card not a Queen is 92.3%
2. What is the probability of the compliment of the event: “Roll a standard die and get an even number”?
There are three even numbers on a standard die: 2, 4, and 6. That means that the probability that you do roll and get an even number is:
Therefore, the complement is:
Earlier Problem Revisited
The complement of an event is the set of all outcomes that are not the event.
What is the probability of the complement to a probability of 74%?
What is the complement to the event: “flipped coin lands on heads”?
"flipped coins land on tails"
What is the probability of the complement of randomly choosing one of the 3 quarters from a set of 10 coins?
For problems 1 – 10, identify the percent probability of the complement of the described event.
- Roll a standard die once and get an even number.
- Pull a red card from a standard deck.
- Pull a face card from a standard deck.
- Roll two standard dice and get a sum greater than 9.
- Pull two cards from a deck, without replacement, get at least one face card.
- Roll a 10-sided die twice, get a 6 both times.
- The probability that a student in your class likes chocolate is 34%.
- Of the 76 students in your math class, 26 earned an A.
- 23% of million-mile cars are Toyotas.
- A candy machine has 24 green, 32 red, and 14 yellow candies in it. You choose a yellow candy.
- There are 150 students in your class, 40 have laptops, and 110 have tablets. 26 of those students have both a laptop and a tablet. What is the probability that a randomly chosen student has a tablet, given that she has a laptop?
- Roll two standard dice, and get 4’s on both, given that you know that you have already rolled a 4 on one of them.
- Draw two cards in a row, without replacement, that are the same suit from a standard deck.
- Roll of two standard dice once, getting a sum greater than 8, given that one of the dice is a 6.
To view the Review answers, open this PDF file and look for section 6.7.