Question

the names of the months are each written on a slip of paper. if a slip of paper is randomly drawn, which scenario depicts mutually exclusive events?
begins with a j and contains a u
ends with an r and has five or fewer letters
has thirty - one days and ends with a y
contains an e and has thirty or fewer days

Explanation:

Step1: Recall mutually exclusive events

Mutually exclusive events cannot occur at the same time. We analyze each option by listing months and their properties.

Step2: Analyze Option 1 (begins with J and contains u)

Months starting with J: January, June, July. January has 'u', so this event is not mutually exclusive.

Step3: Analyze Option 2 (ends with r and five or fewer letters)

Months ending with r: January, February, March, April, May, June, July, August, September, October, November, December? Wait, no: November ends with 'r'? Wait, November is "November" (ends with 'r')? Wait, no, November ends with 'r'? Wait, months: January (7), February (8), March (5), April (5), May (3), June (4), July (4), August (6), September (9), October (7), November (8), December (8). Wait, months ending with 'r': March? No, March ends with 'h'. Wait, no, maybe I made a mistake. Wait, "September" ends with 'r'? No, "September" ends with 'r'? Wait, "September" is S-E-P-T-E-M-B-E-R: yes, ends with 'r'. "October" ends with 'r'? No, "October" is O-C-T-O-B-E-R: yes, ends with 'r'. "November" is N-O-V-E-M-B-E-R: ends with 'r'. "December" is D-E-C-E-M-B-E-R: ends with 'r'. Wait, but five or fewer letters: May (3), April (5), June (4), July (4), March (5). None of these end with 'r' (March ends with 'h', May, April, June, July don't end with 'r'). So months ending with 'r' (September, October, November, December) have more than five letters. So a month can't end with 'r' and have five or fewer letters. So these events are mutually exclusive. Wait, but let's check other options.

Step4: Analyze Option 3 (has 31 days and ends with y)

Months with 31 days: January, March, May, July, August, October, December. Months ending with 'y': January? No, January ends with 'y'? January: J-A-N-U-A-R-Y: yes, ends with 'y'! So January has 31 days and ends with 'y', so not mutually exclusive.

Step5: Analyze Option 4 (contains e and has 30 or fewer days)

Months with 30 or fewer days: February (28/29), April (30), June (30), September (30), November (30). Wait, February: contains 'e'? February: F-E-B-R-U-A-R-Y: yes, contains 'e'. So February has 30 or fewer days and contains 'e', so not mutually exclusive.

So Option 2: ends with r and has five or fewer letters: no overlap, so mutually exclusive. Wait, but let's recheck Option 2. Months with five or fewer letters: May (3), April (5), June (4), July (4), March (5). None end with 'r' (March ends with 'h', May, April, June, July don't end with 'r'). Months ending with 'r' (September, October, November, December) have more than five letters. So no month is in both events. So they are mutually exclusive.

Answer:

ends with an r and has five or fewer letters (the second option)