Biostats 2010 week 1a part 1

Probability

Any probability PA is the event A will happen between 0 and ____.

Sample Space

All possible outcomes must add up to ____ for sample space.

Complement

The probability that an event DOES NOT occur is 1 minus the probability, this is called a ____.

Disjoint

Two events A and B are DISJOINT or ____ if they cannot occur at the same sample space.

Union

A U B which equals A + ____.

Independent

Two events A and B are ____ if knowing that one occurs does NOT change the probability that the other occurs.

Conditional Probability

Probability obtained with the additional information that some other event already occurs is called ____ probability.

Intersection

A upside down U B = A ____ B.

Dependent Events

Dependent events are the probability of one event if we know another event ____.

Non-Disjoint

Non-disjoint events are when there is some sort of ____ between them.

What is the range of any probability PA?

Between 0 and 1

What must all possible outcomes add up to in a sample space?

1

What is the complement of an event?

1 minus the probability of the event occurring

When are two events A and B considered disjoint or mutually exclusive?

When they cannot occur in the same sample space

How do you calculate the probability of A or B occurring?

A + B

What does it mean for two events A and B to be independent?

Knowing that one occurs does not change the probability of the other occurring

How do you denote the intersection of two events A and B?

A upside down U B (A ∩ B)

What is conditional probability?

The probability of an event given that another event has already occurred

How is conditional probability represented?

B|A (B given A)

What does the notation A|B represent?

The probability of A not happening given that B has already occurred

What is the definition of disjoint events?

Two groups that cannot happen at the same time

What is the formula for the union of two non-disjoint events?

P(A) + P(B) - P(A ∩ B)

What is the probability of an event occurring if it is dependent on another event?

It must take into account the occurrence of the first event

How do you calculate the conditional probability of B given A?

P(B|A) = P(A ∩ B) / P(A)

What is the complement of a conditional event?

1 - P(A|B)

What is the significance of the sample space in probability?

It defines all possible outcomes for an event

How do you denote the union of two events A and B?

A U B (A ∪ B)

What is the probability of A and B occurring if they are independent?

P(A) × P(B)

What happens to the sample space when an event occurs without replacement?

The sample space changes, affecting subsequent probabilities

What is the importance of understanding disjoint and non-disjoint events in probability?

It affects how probabilities are calculated and combined.