# Complimentary Events

The event ‘E' and the event ‘not E' are called complementary event of the latter event. If E occurs, its compliment is E which does not occur.

Compliment of an event is denoted by E’ or E or Ec.

For example:

1. When a coin is tossed, getting ‘head’ and getting ‘tail’ are complimentary event of each other.

2. When two coins are tossed, getting ‘atleast one head’ and getting ‘no head’ are complimentary event of each other.

3. When a die is thrown:

Getting ‘even face’ and ‘odd face’ are complimentary event of each other.

Getting ‘multiple of 2’ and getting ‘not multiple of 2’ are complement event of the latter event.

Getting ‘divisible by 3’ and getting ‘not divisible by 3’ are complement event of the latter event.

Sum of the probability of an event ‘E’ and probability of an event ‘not E’ is always 1.

i.e., P(E) + P(not E) = 1

Therefore, P = 1 - P(not E)

Or, P(not E) = 1 - P(E)

Now we will solve the examples on different types of word problems on complementary event.

Problems on complementary event:

1. A bag contains red and what balls. The probability of getting a red ball from the bag of balls is 1/6. What is the probability of not getting a red ball?

Solution:

The probability of getting a red ball from the bag of balls is 1/6.

Therefore, the probability of not getting a red ball

P(ball is not red) = 1 – 1/6 = 5/6

Therefore, the probability of not getting a red ball is 5/6.

2. In a box, contains blue and green marbles. The probability of getting a green marble from the box of marbles is 3/7. What is the probability of getting a blue marble?

Solution:

Let E1 be the event of getting a green marble and

E2 be the event of getting a blue marble

E2 is the probability of getting a blue marble which is also the same as the probability of not getting a green marble, Since we know that the marble are either green or blue.

Therefore, P(not getting a blue marble)

= P(E2) = 1 - P(E1)

= 1 – 3/7

= 4/7.

Therefore, the probability of getting a blue marble is 4/7.

3. In a cricket tournament Yuvraj Singh hits eight times ‘6’ out of thirty two balls. Calculate the probability that he would not hit a 6?

Solution:

Let P(A) = 32be the total number of events .

Favorable events that is Yuvraj Singh hits a boundary P (B) = 8,

Therefore, P(E) = P (Yuvraj Singh hits a ‘6’)

= P(B)/P(A)

= 8/32 = ¼.

Now, P (not E) = P (Yuvraj Singh did not hit a ‘6’) = 1 – 1/4 = 3/4.

4. In a laptop shop there are 16 defective laptops out of 200 laptops. If one laptop is taken out at random from this laptop shop, what is the probability that it is a non defective laptop?

Solution:

The total number of laptops in laptop shop = 200,

The number of defective laptops = 16,

Let E1be the event of getting a defective laptops and
E2 be the event of getting a non defective laptops

P(A) = The probability of getting a defective laptop

= 16/200

= 0.08

Therefore, the probability of getting a non defective laptop = 1 – P(A) = 1 – 0.08 = 0.92.

5. The probability that it will rain in the evening 0.84. What is the probability that it will not rain in the evening?

Solution:

Let E be the event that it will rain in the evening.

Then, (not E) is the event it will rain in the evening .

Then, P(E) = 0.84

Now, P(E) + P(not E) = 1

⇒ P(not E) = 1 - P(E)

⇒ P(not E) = 1 - 0.84

⇒ P(not E) = 0.16

Therefore, the probability that it will not rain in the evening = P(not E) = 0.16

Probability

Probability

Random Experiments

Experimental Probability

Empirical Probability

Coin Toss Probability

Probability of Tossing Two Coins

Probability of Tossing Three Coins

Complimentary Events

Mutually Exclusive Events

Mutually Non-Exclusive Events

Conditional Probability

Theoretical Probability

Odds and Probability

Playing Cards Probability

Probability and Playing Cards

Solved Probability Problems

Probability for Rolling Three Dice

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

## Recent Articles

1. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 13, 24 02:48 AM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

2. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 13, 24 02:23 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

3. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 13, 24 01:20 AM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

4. ### Comparison of Two-digit Numbers | Arrange 2-digit Numbers | Examples

Sep 12, 24 03:07 PM

What are the rules for the comparison of two-digit numbers? We know that a two-digit number is always greater than a single digit number. But, when both the numbers are two-digit numbers