Ch. 2 BioStatistics

Definition:

P(A) is the probability that event A will occur

Example:

If a fair dice is rolled that means that each number is equally likely to occur.

E={2,4,6} even numbers

O={1,3,5} odd numbers

then

P(E)= s/n = 3/6 = 0.5 (s= # of possible successes / n=# of possible outcomes)

Basic Rules of Probability

1. The probability of a certain event is 1
2. The probability of an impossible event is 0
3. Probabilities are between 0 and 1
4. if two events are mutually exclusive i.e. A n B = ~~0~~ then the probability that one or the other will occur is P( A U B ) = P(A) + P(B)
5. The probability that an event will occur added to the probability that the event will not occur is 1 P(A) +P(A’) = 1

Example:

Mutually exclusive events Q and R for which P(Q) = .45 and P(R) = .30 find

1. P(Q’)= 1-.45= .55
2. P( Q U R )= .45+ .3 = .75
3. P(Q n R) = 0
4. P(Q’ n R) = .30

The General Addition Rule

If mutually exclusive A n B = ~~0~~ then P( A1 U A2 ) = P(A1) + P(A2)

This will satisfy any situation: P(AUB) = P(A) + P(B) - P(AnB) or P(AnB) = P(A) + P(B) - P(AUB)

Conditional Probability

P(A I B) is the probability that A occurs given that B has occurred

“s/n”

P(A I B) = P(AnB)/P(B) (true all the time)

Independent Events

If A is independent of B if P(A) = P(B I A) or P(B) = P(B I A)

Works all the time: P(AnB) = P(A I B)P(B)

Only if independent: P(AnB) = P(A)P(B)

True only when independent:

1. P(AnB) = P(A)P(B)
2. P(A) = P(A I B)
3. P(B) = P(B I A)

Always true:

1. P(AnB) = P(A)P(B I A)
2. P(AnB) = P(B)P(A I B)
3. P(AnBnC) = P(A)P(B I A)P(C I AnB)
4. P(AUB) = P(A) + P(B) - P(AnB)
5. P(AnB) = P(A) + P(B) - P(AUB)

Multiplication Principal:

If the choices that an event can occur and definite each step then the equation is (n1)(n2)(n3)…(nk)

Combinations:

nCr=(n r)=(n!)/(n-r)!r!

The order does not matter ex. picking from a basket of apples

Permutation:

nPr=(n!)/(n-r)!

Order matters ex. 5 people getting 5 different drugs, person A getting drug A is different from person A getting drug B.