Determine if the two events are mutually exclusive.
Rolling even numbers on two dice and the dice summing to 7.
Answer
Mutually exclusive.
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.
Answer
Not mutually exclusive.
Example 3
Determine if the two events are mutually exclusive.
Flipping two coins, having the first coin be heads and both coins be tails.
Answer
Mutually exclusive.
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.
Answer
(a) Events A and B are mutually exclusive.
(b) The probability that A or B happens is:
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.
Answer
(a) Events A and B are not mutually exclusive.
(b) The probability that A or B (or both) happens is:
The favorable outcomes are (1, 6), (3, 6), (5, 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...
Answer
(a) Events A and B are mutually exclusive.
(b) The probability that A or B happens is:
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. She 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.
Answer
(a) Events A and B are not mutually exclusive.
(b) The probability that A or B happens is:
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.
Answer
(a) Events A and B are mutually exclusive.
(b) The probability that A or B happens is:
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.
Answer
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?
Answer
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 didn't work out so well. If the probability Jenny wears blue shoes is , what's the probability Jenny wears green shoes?
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.
. 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?
, what's the probability Jenny wears green shoes?