#### 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?

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

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

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

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

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