What is the probability of two persons being born on
the same day (ignoring date)?
(NDA 2008 II)
(a) 1/49
(b) 1/365
(c) 1/7
(d) 2/7
Answers
We have to ignore the date and only consider the days. We know that there are 7 different days.
Consider two persons A and B.
A can be born on any of the 7 days and so can be B. Thus the total no. of outcomes is 7 × 7 = 49.
(Similar to the total no. of outcomes in two dices thrown simultaneously.)
And those 49 total outcomes are given below:
1. Both A and B can be on Sunday.
2. A can be on Sunday and B can be on Monday.
3. A can be on Sunday and B can be on Tuesday.
4. A can be on Sunday and B can be on Wednesday.
5. A can be on Sunday and B can be on Thursday.
6. A can be on Sunday and B can be on Friday.
7. A can be on Sunday and B can be on Saturday.
8. Both A and B can be on Monday.
9. A can be on Monday and B can be on Sunday.
10. A can be on Monday and B can be on Tuesday.
11. A can be on Monday and B can be on Wednesday.
12. A can be on Monday and B can be on Thursday.
13. A can be on Monday and B can be on Friday.
14. A can be on Monday and B can be on Saturday.
15. Both A and B can be on Tuesday.
16. A can be on Tuesday and B can be on Monday.
17. A can be on Tuesday and B can be on Sunday.
18. A can be on Tuesday and B can be on Wednesday.
19. A can be on Tuesday and B can be on Thursday.
20. A can be on Tuesday and B can be on Friday.
21. A can be on Tuesday and B can be on Saturday.
22. Both A and B can be on Wednesday.
23. A can be on Wednesday and B can be on Monday.
24. A can be on Wednesday and B can be on Tuesday.
25. A can be on Wednesday and B can be on Sunday.
26. A can be on Wednesday and B can be on Thursday.
27. A can be on Wednesday and B can be on Friday.
28. A can be on Wednesday and B can be on Saturday.
29. Both A and B can be on Thursday.
30. A can be on Thursday and B can be on Monday.
31. A can be on Thursday and B can be on Tuesday.
32. A can be on Thursday and B can be on Wednesday.
33. A can be on Thursday and B can be on Sunday.
34. A can be on Thursday and B can be on Friday.
35. A can be on Thursday and B can be on Saturday.
36. Both A and B can be on Friday.
37. A can be on Friday and B can be on Monday.
38. A can be on Friday and B can be on Tuesday.
39. A can be on Friday and B can be on Wednesday.
40. A can be on Friday and B can be on Thursday.
41. A can be on Friday and B can be on Sunday.
42. A can be on Friday and B can be on Saturday.
43. Both A and B can be on Saturday.
44. A can be on Saturday and B can be on Monday.
45. A can be on Saturday and B can be on Tuesday.
46. A can be on Saturday and B can be on Wednesday.
47. A can be on Saturday and B can be on Thursday.
48. A can be on Saturday and B can be on Friday.
49. A can be on Saturday and B can be on Sunday.
Among these 49 outcomes, there are only 7 outcomes in which both A and B can be born on same day.
1. Both A and B can be on Sunday.
2. Both A and B can be on Monday.
3. Both A and B can be on Tuesday.
4. Both A and B can be on Wednesday.
5. Both A and B can be on Thursday.
6. Both A and B can be on Friday.
7. Both A and B can be on Saturday.
Thus the no. of favourable outcomes = 7
∴ Probability = 7/49 = ''1/7''
Thus (c) is the answer.
As the number of days in a year is 365
Therefore,number of possible outcomes=365
Also, number of favourable outcomes(two persons being born on same day)=1
As,probability=no. of favourable outcomes/no of possible outcomes
Therefore, probability=1/365
So, here's your answer=1/365