Question

identifying mutually exclusive events

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 o and has thirty or fewer days

Explanation:

Define mutually exclusive events

Using the Mutually Exclusive Events knowledge point
Two events are mutually exclusive if they cannot occur at the same time. In this context, we must find the pair of events for which no single month can satisfy both conditions simultaneously.

Analyze the first option

Using the Mutually Exclusive Events knowledge point

• Event A: The month begins with a 'J'.
• Event B: The month contains a 'u'.
• Let's check the months: January, June, and July all begin with 'J' and contain a 'u'.
• Since these events can occur together, they are not mutually exclusive.

Analyze the second option

Using the Mutually Exclusive Events knowledge point

• Event A: The month ends with an 'r'.
• Event B: The month has five or fewer letters.
• Let's check the months ending in 'r': September (9), October (7), November (8), December (8). None of these have five or fewer letters.
• Therefore, no single month can satisfy both conditions simultaneously. These events are mutually exclusive.

Analyze the third option

Using the Mutually Exclusive Events knowledge point

• Event A: The month has thirty-one days.
• Event B: The month ends with a 'y'.
• Let's check the months ending in 'y': January (31 days), February (28/29 days), May (31 days), July (31 days).
• Since January, May, and July satisfy both conditions, these events are not mutually exclusive.

Analyze the fourth option

Using the Mutually Exclusive Events knowledge point

• Event A: The month contains an 'e'.
• Event B: The month has thirty or fewer days.
• Let's check the months with 30 or fewer days: February (28/29), April (30), June (30), September (30), November (30).
• February, June, September, and November all contain the letter 'e'.
• Since these events can occur together, they are not mutually exclusive.

Answer:

• begins with a J and contains a u
• ends with an r and has five or fewer letters (Correct answer)
• has thirty-one days and ends with a y
• contains an e and has thirty or fewer days