Chapter 14 Part 2

Formal Probability

The sum of probabilities for all possible outcomes of a trial must equal 1.

Example: Flipping a Coin S = {Heads, Tails}

P(H) = 0.5P(T) = 0.5

P(H)+P(T) = 0.5+0.5 = 1

or P(S) = 1

The complement of an event consists of outcomes that are not in the event.

Example:A = roll a 5 or 6 on a die

or A’ = roll a 1, 2, 3, or 4

1)If A = rolling an even on a 6-sided die, what is the complement of A?

2)If B = flipping a coin and landing on Tails, what is the complement of B?

3)If C = passing your class, what is the complement of C?

𝐴𝐶=𝑟𝑜𝑙𝑙𝑖𝑛𝑔𝑎𝑛𝑜𝑑𝑑

𝐵𝐶=𝑙𝑎𝑛𝑑𝑖𝑛𝑔𝑜𝑛𝐻𝑒𝑎𝑑𝑠

𝐶 ′=𝑛𝑜𝑡𝑝𝑎𝑠𝑠𝑖𝑛𝑔 𝑦𝑜𝑢𝑟 𝑐𝑙𝑎𝑠𝑠

The probability of an event not occurring is 1 minus the probability that it does occur.

Data was collected on a stoplight which determined that the light is green 35% of the time. What is the probability that if you approached the stoplight it would not be green?

P(not green) = 1 – P(green) = 1 - 0.35

= 0.65

Events are independent if one does not affect the other.

Example of Independent Events Rolling a 5 and then rolling a 6: the probability of rolling a 6 on the second roll is not affected by whether or not the first roll was a 5

Example of Dependent Events Drawing a King on the first draw and then a King on the second draw: the probability of drawing a King on the second draw depends on if a King was drawn already removed from the deck

Disjoint (often called mutually exclusive) events have no outcomes in common.

Disjoint Events: A = drawing a face card B = drawing a 2

Not Disjoint Events: A = drawing a face card B = drawing a diamond

Notation: (A or B)(A and B)

For two events that are disjoint, the probability that either one or the other

occurs is the sum of the probabilities of each event.

The same stoplight from the earlier example that has a 35% chance of being green also has a 4% chance of being yellow and 61% chance of being red. What is the probability that when you cross paths with the light, it is yellow or green?

P(yellow green) = P(yellow) + P(green) = 0.35 + 0.04 = 0.39

For two independent events A and B, the probability that both will occur is the product

of each probability.

What is the probability of rolling a 6 on a single die twice in a row?

Suppose that 40% of cars in your area are manufactured in the United States, 30% in Japan, 10% in Germany, and 20% in other countries. If cars are selected at random, find the probability that: 1)A car is not U.S. made

2)It is made in Japan or Germany

3)You see two in a row from Japan

1-P(made in U.S.) = 1 – 0.4 = 0.6

P(G) + P(J) = 0.3 + 0.1 = 0.4

P(JJ) = P(J)P(J) = (0.3)(0.3) = 0.09

Suppose that 40% of cars in your area are manufactured in the United States, 30% in Japan, 10% in Germany, and 20% in other countries. If cars are selected at random, find the probability that: 1)None of three cars came from Germany

2)At least one of three cars is U.S. made

3)The first Japanese car is the 4th one chosen

P() = (.9)(.9)(.9) = 0.729

1-P() = 1 – (.6)(.6)(.6) = 0.784

P() = (.7)(.7)(.7)(.3) = 0.1029

Law of Averages – NO!A couple just had their 5th child, another boy! All 5 of their children have been boys. They

thought that after having 4 boys, the 5th child HAD to be a girl because of the law of

averages!

The Law of Averages is not a real thing! Every child has a 50% chance of being genetically male and a 50% chance of being genetically

female, regardless of the gender of the children that came before.

Today’s Assignment: Worksheet Add to HW #9 page 338 #6-8, 19-24, 31,

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