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# Probability and Statistics

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# Mutually Exclusive Events Exercises

### Example 1

Determine if the two events are mutually exclusive.

Rolling even numbers on two dice and the dice summing to 7.

### Example 2

Determine if the two events are mutually exclusive.

Pulling an ace from a deck of cards and, without replacing the ace, pulling another ace from the deck. Assuming the person pulling the aces is not David Copperfield.

### Example 3

Determine if the two events are mutually exclusive.

Flipping two coins, having the first coin be heads and both coins be tails.

### Example 4

For the following pair of events, (a) determine if the two events A and B are mutually exclusive, and (b) find the probability that A or B (or both) happens.

You flip one coin.

Event A: you get heads.

Event B: you get tails.

### Example 5

For the following pair of events, (a) determine if the two events A and B are mutually exclusive, and (b) find the probability that A or B (or both) happens.

You roll two dice.

Event A: The first die shows an odd number.

Event B: The second die shows the number 6.

### Example 6

For the following pair of events, (a) determine if the two events *A* and *B* are mutually exclusive, and (b) find the probability that A or B (or both) happens.

You roll two dice.

Event A: The dice sum to 5.

Event B: The dice sum to 8.

Hey, something's not adding up here...

### Example 7

Penny has a green shirt, a purple shirt, and a red shirt. Seemingly, she shops at the same place where Jenny bought her shoes. Penny also has black pants and blue pants. She picks a shirt at random and picks a pair of pants at random. What an appearance-conscious fashionista she is.

Hey, it was dark when she got dressed. Cut her some slacks.

Event A: Penny wears a green shirt.

Event B: Penny wears black pants.

### Example 8

Same deal as above: Penny has a green shirt, a purple shirt, and a red shirt. She has black pants and blue pants. She picks a shirt at random and picks a pair of pants at random.

Event A: Penny wears a green shirt.

Event B: Penny wears a red shirt.

### Example 9

A spinner for the game of Twister has four colors: red, blue, yellow, and green. If the spinner is a little wobbly and has a probability of of landing on red, what is the probability that the spinner doesn't land on red? Careful...your entire sense of balance depends on getting this question right.

### Example 10

A frog will catch his next fly with probability . He could probably catch more flies with honey, but his pantry is currently empty. What is the probability that the frog will miss his next fly?

### Example 11

Jenny has blue shoes and green shoes. She can only wear one color of shoes at a time, and she must wear shoes. She gave barefoot a try one day last week and it did not work out so well. If the probability Jenny wears blue shoes is , what is the probability Jenny wears green shoes?