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Probability and Statistics

Probability and Statistics

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

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.

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

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.

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?

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