Misc 9 - If 4-digit numbers greater than 5,000 are randomly - Using permutation

Slide32.JPG
Slide33.JPG Slide34.JPG Slide35.JPG Slide36.JPG Slide37.JPG Slide38.JPG Slide39.JPG Slide40.JPG Slide41.JPG

  1. Chapter 16 Class 11 Probability
  2. Serial order wise
Ask Download

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)﷯ = 99﷮249﷯ = 𝟑𝟑﷮𝟖𝟑﷯ 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)﷯ = 18﷮48﷯ = 𝟑﷮𝟖﷯

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail