Chapter 6 Day 2

Multiplication Principle – if you do one task a number of ways and a second task b number of ways, then both tasks can be done a x b number of ways. Multiplication Principle – if you do one task a number of ways and a second task b number of ways, then both tasks can be done a x b number of ways. You are creating a password for you phone. The password must be 4 digits long. How many possible passwords could you make? You are creating a password for you phone. The password must be 4 digits long. How many possible passwords could you make?

Now, think of flipping a coin 6 times. What is the size of the sample space? Now, think of flipping a coin 6 times. What is the size of the sample space? Suppose you are only concerned with the number of heads flipped. What is the sample space? Suppose you are only concerned with the number of heads flipped. What is the sample space?

Probability Rules Rule 1: The probability P(A) of any event satisfies Rule 1: The probability P(A) of any event satisfies 0 ≤ P(A) ≤1 Rule 2: If S is the sample space in a probability model, then P(S) = 1 Rule 2: If S is the sample space in a probability model, then P(S) = 1 Rule 3: The complement of any event A is the event that A does not occur, written as A c. The complement rule states that Rule 3: The complement of any event A is the event that A does not occur, written as A c. The complement rule states that P(A c ) = 1 – P(A) Rule 4: Two events A and B are disjoint if they have no outcomes in common and so can never occur simultaneously. If A and B are disjoint, Rule 4: Two events A and B are disjoint if they have no outcomes in common and so can never occur simultaneously. If A and B are disjoint, P(A or B) = P(A) + P(B) This is the addition rule for disjoint events.

Complementary Sets

Disjoint Events

Example A basket contains 4 red markers, 2 green markers, and 1 black marker. Find the following probabilities: A basket contains 4 red markers, 2 green markers, and 1 black marker. Find the following probabilities: P(green) P(green) P(green and red) P(green and red) P(green or red) P(green or red) P(not black) P(not black)

If woman age 25 to 29 was selected at random and asked her marital status it would follow the probability model below. If woman age 25 to 29 was selected at random and asked her marital status it would follow the probability model below. What is the probability that a woman selected at random is not married? What is the probability that a woman selected at random is not married? What is the probability that a woman selected at random is either never married or divorced? What is the probability that a woman selected at random is either never married or divorced? Marital Status Never Married MarriedWidowedDivorced Probability

Multiplication Rule for Independent Events Rule 5: Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent Rule 5: Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent P(A and B) = P(A)P(B)

Examples In a standard deck of cards, what is the probability that you choose a heart, replace it, and then an ace? In a standard deck of cards, what is the probability that you choose a heart, replace it, and then an ace? A jar contains 7 black marbles, 8 white marbles, and 3 green marbles. What is the probability that you select a white marble, replace it, and then select a green marble? A jar contains 7 black marbles, 8 white marbles, and 3 green marbles. What is the probability that you select a white marble, replace it, and then select a green marble?