**Complement of an event worksheet :**

Worksheet on compliment of an event is much useful to the students who would like to practice problems on complement probability.

We can apply probabilities to situations involving random selection, such as drawing a card out of a shuffled deck or pulling a marble out of a closed bag.

1. There are 2 red jacks in a standard deck of 52 cards. What is the probability of not getting a red jack if you select one card at random ?

2. A jar contains 8 marbles marked with the numbers 1 through 8. If you pick a marble at random, what is the probability of not picking the marble marked with the number 5 ?

**Problem 1 :**

There are 2 red jacks in a standard deck of 52 cards. What is the probability of not getting a red jack if you select one card at random ?

**Solution : **

**Step 1 : **

P(event) + P(complement) = 1

P(red jack) + P(not a red jack) = 1

**Step 2 : **

The probability of getting a red jack is 2/52.

Substitute 2/52 for P(red jack).

2/52 + P(not a red jack) = 1

**Step 3 : **

Subtract 2/52 from both sides.

[2/52 + P(not a red jack)] - 2/52 = 1 - 2/52

P(not a red jack) = 52/52 - 2/52

P(not a red jack) = (52 - 2)/52

P(not a red jack) = 50/52

Simplify.

P(not a red jack) = 25/26

The probability that you will not draw a red jack is 25/26 . It is likely that you will not select a red jack.

**Problem 2 :**

A jar contains 8 marbles marked with the numbers 1 through 8. If you pick a marble at random, what is the probability of not picking the marble marked with the number 5 ?

**Solution : **

**Step 1 :**

P(event) + P(complement) = 1

P(marble numbered 5) + P(not the marble numbered 5 ) = 1

**Step 2 :**

The probability of getting a marble numbered 5 is 1/8.

Substitute 1/8 for P(marble numbered 5).

1/8 + P(not the marble numbered 5) = 1

**Step 3 :**

Subtract 1/8 from both sides.

[1/8 + P(not the marble numbered 5)] - 1/8 = 1 - 1/8

P(not the marble numbered 5) = 8/8 - 1/8

P(not the marble numbered 5) = (8 - 1)/8

P(not the marble numbered 5) = 7/8

The probability that you will not pick a marble numbered with 5 is 7/8 . It is likely that you will not pick a marble numbered with 5.

After having gone through the stuff given above, we hope that the students would have understood "Complement of an event worksheet".

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