I already have the answers for these bits, the thing is I'm unable to understand and grasp its concept, so I sincerely request someone to send a detailed, well explained step by step answer
Answers
Answer:
Let me give you an example to make you understand the concept behind the calculation.
Let's say that cards are number from 2 to 11 and are put in a box.
Total number of cards would be calculated to be 10 if you count by fingers. But our math proves it to be 9 which is obtained by 11 - 2. This is the place where logic comes to our rescue.
When we subtract 2 from 11, we generally dont include 11 in the difference due to which it is left without getting subtracted. In our case, it is give that cards from 2 to 11 are inside the box. This means that 11 is also included in the box.
Therefore we must add 1 at the end after calculating the difference to get the accurate answer.
⇒ 11 - 2 + 1
⇒ 9 + 1 = 10
Now coming to your question, it is given that cards from 2 to 101 are put in a box. This means 101 and 2 both are included. Therefore we need to calculate the difference and add 1 to the final answer.
Difference: 101 - 2 = 99
Final Answer = 99 + 1 = 100 cards.
Hence the Sample Space of this experiment is 100.
1 ) Number less than 14
Here, the word 'less than' is important. This means that we must not include 14 but we can include all the other numbers. Hence the number of such cards would be:
- 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 = 12 cards
⇒ Probability = 12 / 100 = 0.12
2 ) Number which is a perfect square
- Perfect Squares: 4, 9, 16, 25, 36, 49, 64, 81, 100 = 9
⇒ Probability = 9 / 100 = 0.09
3 ) Prime number less than 20
- 2, 3, 5, 7, 11, 13, 17, 19 = 8
⇒ Probability = 8 / 100 = 0.08
4 ) A multiple of 5
- 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 = 20
⇒ Probability = 20 / 100 = 0.2