# Misc 9

Last updated at March 9, 2017 by Teachoo

Last updated at March 9, 2017 by Teachoo

Transcript

Misc 9 If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? Digit number greater than 5000 can be formed with either 5 in beginning or 7 in beginning . Let A be the event that this number is divisible by 5 A number is divisible by 5 in the following cases For (a) Total no of cases = 1 × 5 × 5 × 1 = 25 For(b) Total no. of cases = 1 × 5 × 5 × 1 = 25 For (c) Total no of cases = 1 × 5 × 5 × 1 = 25 But if we get all 0’s after 5, we will get 5000. But we want number greater than 5000 Number of cases = 25 – 1 = 24 For(d) Total no. of cases = 1 × 5 × 5 × 1 = 25 Hence, Total numbers divisible by 5 = 25 + 25 + 24 + 25 = 99 So, n(A) = 99 Hence, P(A) = n(A)n(S) = 99249 = 𝟑𝟑𝟖𝟑 Misc 9 If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (ii) the repetition of digits is not allowed? Digit number greater than 5000 can be formed with either 5 in beginning or 7 in beginning . Let B the event that the number greater than 5000 is divisible by 5 Hence it should have either 5 or 0 at unit place A number is divisible by 5 in the following cases For (b) Total number of cases = 1 × 3 × 2 × 1 = 6 For (c) Total number of cases = 1 × 3 × 2 × 1 = 6 For (d) Total number of cases = 1 × 3 × 2 × 1 = 6 Hence Total number of cases when digit is divisible by 5 = 6 + 6 + 6 = 18 So, n(B) = 18 Hence, P(B) = n(B)n(S) = 1848 = 𝟑𝟖

Class 11

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.