Exam 4: Probability and Probability Distributions

The law of large numbers states that subjective probabilities can be estimated based on the long run relative frequencies of events

The relative frequency of an event is the number of times the event occurs out of the total number of times the random experiment is run.

If A and B are mutually exclusive events with P(A)= 0.30 and P(B)= 0.40,then the probability that either A or B occur is:

Two events A and B are said to be independent if P(A and B)= P(A)+ P(B)

Probabilities that cannot be estimated from long-run relative frequencies of events are

If A and B are independent events with P(A)= 0.40 and P(B)= 0.50,then P(A/B)is 0.50.

If A and B are two independent events with P(A)= 0.20 and P(B)= 0.60,then P(A and B)= 0.80

If P(A)= P(A|B),then events A and B are said to be

Two or more events are said to be exhaustive if at most one of them can occur.

Probabilities that can be estimated from long-run relative frequencies of events are

The probability of an event and the probability of its complement always sum to

The number of car insurance policy holders is an example of a discrete random variable.

Two or more events are said to be exhaustive if one of them must occur.

If two events are mutually exclusive,what is the probability that one or the other occurs?

A discrete probability distribution:

The probabilities shown in a table with two rows, $A _ { 1 } \text { and } A _ { 2 }$ And two columns, $B _ { 1 } \text { and } B _ { 2 }$ ,are as follows: $P \left( A _ { 1 } \text { and } B _ { 1 } \right) = 10$ , $P \left( A _ { 1 } \text { and } B _ { 2 } \right) = .30$ , $P \left( A _ { 2 } \text { and } B _ { 1 } \right) = .05$ ,and $P \left( A _ { 2 } \text { and } B _ { 2 } \right) = .55$ )Then $P \left( A _ { 1 } \mid B _ { 1 } \right)$ ,calculated up to two decimals,is