Question

Numbers from 1 to 80 are written on separate cards and put in a box one of the cards is randomly selected. What is the probability that the card selected is either and even number in all the cards present or an odd number under 10

Answer 1

`(9)/(16)`

Explanation:

We are given that there are a total of 80 possibilities when a card a chosen from the box which has separate cards numbered from 1 to 80.

Case 1: Number of possible cases for even number to be chosen:

`(80)/(2) = 40`

because from number 1 to 80, there will be a total of 40 even numbers
`(2, 4, 6, 8, 10, ... , 80)`

Case 2: Number of cases for an odd number below 10:

`5` because below 10, the odd number possible are
`(1,3,5,7,9)`

So, the total number of favorable cases as per the question = 45

Total Number of cases = 80

`\text {Probability} = \frac{\text{Total Number of Favorable Cases}}{\text{Total Number of Cases}}\\\Rightarrow (45)/(80)\\\Rightarrow (9)/(16)`

So, required probability is
`(9)/(16)`
`.`