Define the terms.

Sample Space -

Event -

Mapping -

RF -

Probability the Range of Probability -

Range of Probability 0<=P(A),=1 -

Unusual Event -

Mutually Exclusive -

Compliment -

The rule of Complement Addition rule of Probabilities -

Conditional Probability -

Addition rule of Probability with Mutually Exclusive events -

Compounds events -

Independent event -

Random Selection -

Problems

A fair dice is rolled, the sample space is 1 2 3 4 5 6 find P(2), P(Even numbers), P(less than 3), P(greater than 2), P(7) and P(less than 10)

If a toss a coin twice are you certain to get one head and one tail?

If you toss a coin 100 time are you certain to get 50 heads and 50 tails?

If you toss a coin more and more and more will the proportion of heads reach 0.5?

Assuming the coin is tossed twice the coin may not be fair, is the following model of probability. Is TRUE

Outcome HH HT TH TT

Probability 0.55 0.42 0.31 0.25

Probability 0.36 0.24 0.24 0.16

Probability 0.33 -1,2 0.33 0.01

A dice is rolled, event A `is that the dice comes up with 3 and event B is that the dice comes up with an even number. Are the events Mutually exclusive?

Addition of Rule of Probabilities P(A Or B) = P(A) +P(B) - P(A and B) for mutually exclusive events the last part P(A and B) is zero, why?

Compute the probability In Math115 class of 2023 out of 45 students 11 got A, 22 got B and 8 got a C grade in the final exam.

A. what is the probability that a randomly selected student got an A OR a B?

B. What is the probability that a randomly selected student got an A or a B or a C?

1. If P(A) = 0.75, P(B) = 0.4 and P(A and B) = 0.25 find P(A or B)

1. If P(A) = 0.2 and P(B) = 0.5 A and B Mutually Exclusive (ME), find P(A or B)

1. If P(A) = 0.3, P(B) = 0.4 and P(A and B) = 0.7 are A and B ME?

1. If P(A) = 0.5, P(B) = 0.4 and P(A or B) = 0.8 are A and B ME?

1. If P(A) = 0.35 find P(A') =?

1. If P(A) = P(A") find P(A)? and if P(B") =0.64 find P(B)?