COMPLEMENT OF AN EVENT WORKSHEET

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 ?

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 ?

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. 

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.