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

Events in 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

Probability for Rolling Two Dice

Solved Probability Problems

Probability for Rolling Three Dice







9th Grade Math

From Complimentary Events to HOME PAGE




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.



New! Comments

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




Share this page: What’s this?

Recent Articles

  1. Worksheet on Mixed Addition and Subtraction | Questions on Addition

    Jan 12, 25 02:14 PM

    In worksheet on mixed addition and subtraction the questions involve both addition and subtraction together; all grade students can practice the questions on addition and subtraction together.

    Read More

  2. Estimating Sums and Differences | Estimations | Practical Calculations

    Jan 12, 25 02:02 PM

    Estimating Difference
    For estimating sums and differences in the number we use the rounded numbers for estimations to its nearest tens, hundred, and thousand. In many practical calculations, only an approximation is requir…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jan 12, 25 01:36 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Checking Subtraction using Addition |Use Addition to Check Subtraction

    Jan 12, 25 01:13 PM

    Checking Subtraction using Addition Worksheet
    We can check subtraction by adding the difference to the smaller number. Since the sum of difference and smaller number is equal to the larger number, subtraction is correct.

    Read More

  5. Worksheet on Subtraction of 4-Digit Numbers|Subtracting 4-Digit Number

    Jan 12, 25 09:04 AM

    Worksheet on Subtraction of 4-Digit Numbers
    Practice the questions given in the worksheet on subtraction of 4-digit numbers. Here we will subtract two 4-digit numbers (without borrowing and with borrowing) to find the difference between them.

    Read More