Solve Complementary Events
Probability is the chance of the outcome of an event of a particular experiment. An event is a one or more possible outcomes of an experiment. Probabilities are occurs always numbers between 0(impossible) and 1(possible). The set of all possible outcomes of a particular experiment is called sample space.
Complementary Events:
When one event occurs if and only if the other event does not occur, they are called complementary events. The sum of probabilities of complementary events = 1. i.e P(A) + P(A') = 1
Solve Complementary Events - Example Problems
See these solved problems to understand about complementary events.
Example 1: A bag has 9 green balls and 11 blue balls, if 3 balls are drawn at random, what is the probability of not getting all the 3 are green balls?
Solution:
Let S be the sample space = 9 + 11 = 20
A be the event of getting all the 3 are green balls.
n(S) = C(20,3) = 1140
n(A) = C(9,3) = 84
P(A) = `84/1140` = `7/95`
P(A') = 1 - P(A)
= 1 - `7/95` = `88/95`.
Therefore the probability of not getting all the 3 are green balls is `88/95` .
Example 2: If the probability of a complementary event is `2/7`, what is the probability of an event occurring?
Solution:
P(A) = 1 - P(A')
= 1 - `2/7` = `5/7`.
Therefore the probability of an event occurring is `5/7`.
Example 3: A bag has 7 fifty dollar bills and 10 hundred dollar bills, if 2 bills are drawn at random, what is the probability of getting both are hundred dollar bills and its complementary event?
Solution:
Let S be the sample space = 7 + 10 = 17
A be the event of getting 2 hundred dollar bills.
n(S) = C(17,2) = 136
n(A) = C(10,2) = 45
P(A) = `45/136`
P(A') = 1 - P(A)
= 1 - `45/136` = `91/136`. I have recently faced lot of problem while learning multiplication table chart, But thank to online resources of math which helped me to learn myself easily on net.
Solve Complementary Events - Practice Problems
Solve these following practice problems.
Problem 1: A bag has 8 green balls and 7 blue balls, if 3 balls are drawn at random, what is the probability of not getting all the 3 are blue balls?
Problem 2: If the probability of a complementary event is `3/10`, what is the probability of an event occurring?
Answer: 1) `1/13` 2) `7/10`
Probability is the chance of the outcome of an event of a particular experiment. An event is a one or more possible outcomes of an experiment. Probabilities are occurs always numbers between 0(impossible) and 1(possible). The set of all possible outcomes of a particular experiment is called sample space.
Complementary Events:
When one event occurs if and only if the other event does not occur, they are called complementary events. The sum of probabilities of complementary events = 1. i.e P(A) + P(A') = 1
Solve Complementary Events - Example Problems
See these solved problems to understand about complementary events.
Example 1: A bag has 9 green balls and 11 blue balls, if 3 balls are drawn at random, what is the probability of not getting all the 3 are green balls?
Solution:
Let S be the sample space = 9 + 11 = 20
A be the event of getting all the 3 are green balls.
n(S) = C(20,3) = 1140
n(A) = C(9,3) = 84
P(A) = `84/1140` = `7/95`
P(A') = 1 - P(A)
= 1 - `7/95` = `88/95`.
Therefore the probability of not getting all the 3 are green balls is `88/95` .
Example 2: If the probability of a complementary event is `2/7`, what is the probability of an event occurring?
Solution:
P(A) = 1 - P(A')
= 1 - `2/7` = `5/7`.
Therefore the probability of an event occurring is `5/7`.
Example 3: A bag has 7 fifty dollar bills and 10 hundred dollar bills, if 2 bills are drawn at random, what is the probability of getting both are hundred dollar bills and its complementary event?
Solution:
Let S be the sample space = 7 + 10 = 17
A be the event of getting 2 hundred dollar bills.
n(S) = C(17,2) = 136
n(A) = C(10,2) = 45
P(A) = `45/136`
P(A') = 1 - P(A)
= 1 - `45/136` = `91/136`. I have recently faced lot of problem while learning multiplication table chart, But thank to online resources of math which helped me to learn myself easily on net.
Solve Complementary Events - Practice Problems
Solve these following practice problems.
Problem 1: A bag has 8 green balls and 7 blue balls, if 3 balls are drawn at random, what is the probability of not getting all the 3 are blue balls?
Problem 2: If the probability of a complementary event is `3/10`, what is the probability of an event occurring?
Answer: 1) `1/13` 2) `7/10`
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