Question

Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of
Getting a number 6?
Getting a number less than 6?
Getting a number greater than 6?
Getting a 1-digit number?

Answer 1

Hint: When we take a slip from the box of slips numbered from 1 to 10, we get any number randomly between 1 to 10.

From the given information numbers written on slips are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.
Probability of an Event E = (Number of favorable outcomes) / (Total number of outcomes)
Number 6
Number of favorable outcomes = 1
Probability of getting number 6 = 1/10
Numbers less than 6 are 1, 2, 3, 4 and 5.
Number of favorable outcomes = 5
Probability of getting a number less than 6 = 5/10
The numbers greater than 6 are 7, 8, 9 and 10.
Number of favorable outcomes = 4
Probability of getting number greater than 6 = 4/10 2/5
From 1 to 10 numbers except 10 remaining 9 numbers are single digit numbers.
Number of favorable outcomes = 9
Probability of getting a single digit number = 9/10

Note:
Probability is a measure of how often a particular event will happen if some experiment is done. Probability of an event E = P(E)=n(E)/ n(S). n(E) is the number of favorable outcomes to the event E. n(S) is the total number of outcomes in sample space. For example tossing a coin is an experiment. We get outcomes as Head and tails. So Sample space contains these 2 outcomes. Now if we want the probability of head, this will be our event. Then the number of favorable outcomes of our event is 1.
Probability becomes equal to ½.