Question

1. determine whether these events are mutually exclusive.

a. roll two dice: get a sum of 7 or get doubles.
b. select a student in your college: the student is a sophomore and the student is a business major.
c. select any course: it is a calculus course and it is an english course.
d. select a registered voter: the voter is a republican and the voter is a democrat.

Explanation:

• For part a:
• Mutually - exclusive events cannot occur at the same time.
• When rolling two dice, the event of getting a sum of \(7\) (e.g., \((1,6)\), \((2,5)\), \((3,4)\), \((4,3)\), \((5,2)\), \((6,1)\)) and the event of getting doubles (e.g., \((1,1)\), \((2,2)\), \((3,3)\), \((4,4)\), \((5,5)\), \((6,6)\)) have no common outcomes. So, they are mutually exclusive.
• For part b:
• A student can be a sophomore and a business major simultaneously. So, these events are not mutually exclusive.
• For part c:
• A course cannot be a calculus course and an English course at the same time. So, these events are mutually exclusive.
• For part d:
• A voter cannot be a Republican and a Democrat at the same time. So, these events are mutually exclusive.

Answer:

a. Mutually exclusive.
b. Not mutually exclusive.
c. Mutually exclusive.
d. Mutually exclusive.