Intro To Probability

Usually given by a S - list the outcomes

EXAMPLES:

1. One Coin Experiment: flipping a coin Sample Space: {H, T}
2. Two Fuses Experiment: pulling out defective or undefective fuse Sample Space: {NN, ND, DN, DD}
3. Selects two fuses and records how many are defective S = {0, 1, 2}

4. Records the Number of Fuses inspected until the second defective is found S = {2, 3, 4, …}

   Two is the soonest it can be found cant be before 2.

Event - can be just one outcome or a collection of outcomes in a sample space.

EXAMPLES:

1. Flip A Coin S : {H, T} Let Event A = Getting Tails (P)robability(A) = 1/2

   Note - You can divide by total number of outcomes only if they are equally likely.

2. Roll a die S : {1,2,3,4,5,6} Let Event A = Getting a 5 P(A) = 1/6
3. Select Random Card S : {deck of 52 cards} Let A to be getting a king P(A) = 4/52 = 1/13

The Compliment of an event A is deonted as A^C

A^C contains outcomes NOT in A

EXAMPLE: Let Event A = [3, 6] So, A^c = {1,2,4,5} P(A) = 2/6 P(A^c) = 4/6 P(A) + P(A^c) = 1

General Addition Rule P(AUB) = P(A) + P(B) - P(AnB)