find odda of evenet

Question

Seven slips of paper marked with the numbers 1,2,3,4,5,6,7 are placed in a box and mixed well. Two are drawn what are the odds in favor of the sum of the numbers on the two selected slips is not 5?

Answer 1

First find the number of all possible events. In this case combination is used since the order in which the numbers are selected does not matter, i.e., (2, 6) is the same as (6, 2).

 

₇C₂ = 21

 

Now find the number of events in which the sum IS 5.

 

(1, 4) and (2, 3)  Just like above there are only two not four events.

 

So the probability of getting a 5 is 2/21.

The probability of NOT getting a five is 1 - 2/21, or 19/21.

Answer 2

To find the odds of not getting a 5 we would find:

1 - probability of getting a five

 

The probability of getting a five would be 1/7 for our first draw and 1/6 for our second draw.

 

Since drawing a five could happen on either our first "or" our second draw, the "or" tells us to add these probabilities.

 

1/7 + 1/6

6/42 + 7/42

13/42

 

This is the odd of getting a 5

 

So not getting a five is:

 

1 - 13/42 = 29/42