17.a Probability

Question 1

What is the probability equation?

Answer 1

Question 2

What is the probability if an outcome can NOT occur?

Answer 2

0

Question 3

What is the probability if an outcome HAS TO occur?

Answer 3

1

Question 4

What does “sample space” mean?

Answer 4

The set of all possible outcomes of the experiment

Question 5

What is the sum of the probabilities of every outcome in a sample space?

Answer 5

1

Question 6

What is the sample space and probability of tossing a fair coin twice?

Answer 6

Question 7

What are “complementary events”

Answer 7

In an experiment two events that share no common outcomes but together count every possible outcome are said to be COMPLEMENTARY

-> If one occurs, the other does NOT occur

Question 8

If two events are complementary, knowing the probability that one event occurs allows you to….

Answer 8

Calculate the probability of the other event occuring!

P(A) + P(Not A) = 1

Question 9

What do you do in probability with the word “and”

Answer 9

When dealing with independent events, the word “and” means you multiply

Question 10

Solve:

Answer 10

Question 11

Why is a flip of a coin an independent event

Answer 11

Because whatever happens, every flip is not connection nor influenced by the flip before or after it

Question 12

What is a dependent event?

Answer 12

When two events, A and B, are dependent if the occurrence of the first event affects the occurrence of the second event in such a way that the probability of the second event is changed

Question 13

Given A and B are dependent events, what is the formula for P(A and B) ?

Answer 13

Probability of event A * Probability of event B given A has already occurred

Question 14

Solve:

Answer 14

Question 15

How could event A and B be mutually exclusive?

Answer 15

If event A and event B can NOT occur together!

Question 16

What is the addition rule concerning mutually exclusive events?

Answer 16

If the events are mutually exclusive, add the probabilities together and you will have the probability that either of the events occurs.

Question 17

Solve:

Answer 17

Question 18

What is the addition rule concerning NON-mutually exclusive events?

Answer 18

Question 19

Solve:

Answer 19

Question 20

How would you solve this:

A fair coin is flipped 3 times, what is the probability that the coin lands on heads exactly two times?

Answer 20

Question 21

When can you use this shortcut using permutations:

(# of outcomes producing the event) x (probability of one outcome)

Answer 21

ONLY when EACH of the outcomes have the SAME probability!

Question 22

Solve:

Answer 22

Question 23

How would you solve an “at least” problem?

“a fair coin is tossed 3 times. What is the probability that it lands on heads AT LEAST two times?”

Answer 23

Calculate the probability of the mutually exclusive scenarios first,
and add those probabilities together!

Question 24

Explain how you would solve this?

Answer 24

Question 25

How do you solve a problem asking you what the probability is of it happening "at least once"?

Answer 25

P(at least 1 outcome occurs) = 1 - P(none of these outcomes occur)

Question 26

Solve:

Answer 26

Question 27

Does this equal 1?

Answer 27

NO. Do not forget the probability of selecting 1 red marble, these two events alone are not complementary events