# 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

About the Author

CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .