I took a quiz for my statistics/data class and one of the questions was:
Which of the following pairs of events is mutually exclusive?
- Drawing a face card or drawing a queen from a deck of cards
- Rolling doubles or rolling a total of 6 with two standard dice
- Spinning a prime number or spinning an even number on a spinner with eight sectors numbered from 1 to 8
- Rolling a number greater than 3 or rolling an even number with a fair die
I used process of elimination and selected number 3. as my answer. I got it wrong and my teacher said that number 4 is the correct answer. Unfortunately, the class is all online so I didn't really understand his explanation as well as I would have in an in-person class.
Can someone explain how number 4 is a mutually exclusive event? I would assume that you can roll a number greater than 3 and an even number at the same time.
You are correct, none of these are mutually exclusive pairs of events. Their intersections are, in order: drawing a queen of any suit, rolling $(3, 3)$, spinning a $2$, and rolling either a 4 or a 6. Either you have copied the problem incorrectly, or the problem (and thus necessarily your teacher's explanation) is wrong.