Question

Find out the birthday (month and day but not year) of a randomly chosen person. What is the sample space of the experiment? How many outcomes are in the event that the person is born in July?

Solution

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Step 1

1 of 2

Since, the birthday can be in any month and on any day.

Hence, there will be 365 OR 366(Leap Year) outcomes.

Let's assume the following:

  1. Jan\textbf{Jan} represents January, Feb\textbf{Feb} represents February, Mar\textbf{Mar} represents March, Apr\textbf{Apr} represents April, May\textbf{May} represents May, Jun\textbf{Jun} represents June, Jul\textbf{Jul} represents July, Aug\textbf{Aug} represents August, Sep\textbf{Sep} represents September, Oct\textbf{Oct} represents October, Nov\textbf{Nov} represents November, Dec\textbf{Dec} represents December.

  2. Days of the months are represented by corresponding numerical values.

Hence, the sample space S = {1 Jan, 2 Jan, . . ., 30 Jan, 31 Jan,1 Feb, 2 Feb, . . ., 28 Feb, 29 Feb (Only in case of leap year),1 Mar, 2 Mar, . . ., 30 Mar, 31 Mar,1 Apr, 2 Apr, . . ., 30 Apr,1 May, 2 May, . . ., 30 May, 31 May,1 Jun, 2 Jun, . . ., 30 Jun,1 Jul, 2 Jul, . . ., 30 Jul, 31 Jul,1 Aug, 2 Aug, . . ., 30 Aug, 31 Aug,1 Sep, 2 Sep, . . ., 30 Sep,1 Oct, 2 Oct, . . ., 30 Oct, 31 Oct,1 Nov, 2 Nov, . . ., 30 Nov,1 Dec, 2 Dec, . . ., 30 Dec, 31 Dec } \textbf{S = \{\\ 1 Jan, 2 Jan, . . ., 30 Jan, 31 Jan,\\ 1 Feb, 2 Feb, . . ., 28 Feb, 29 Feb (Only in case of leap year),\\ 1 Mar, 2 Mar, . . ., 30 Mar, 31 Mar,\\ 1 Apr, 2 Apr, . . ., 30 Apr,\\ 1 May, 2 May, . . ., 30 May, 31 May,\\ 1 Jun, 2 Jun, . . ., 30 Jun,\\ 1 Jul, 2 Jul, . . ., 30 Jul, 31 Jul,\\ 1 Aug, 2 Aug, . . ., 30 Aug, 31 Aug,\\ 1 Sep, 2 Sep, . . ., 30 Sep,\\ 1 Oct, 2 Oct, . . ., 30 Oct, 31 Oct,\\ 1 Nov, 2 Nov, . . ., 30 Nov,\\ 1 Dec, 2 Dec, . . ., 30 Dec, 31 Dec \} } (ANS)

If we see, there are 31 days in July Hence, if a person is born in July, there will be 31 Outcomes\boxed{\textbf{31 Outcomes}}

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