Chapter 5.2

A standard deck of cards contains 52 cards. One card is selected from the deck. ​(a) Compute the probability of randomly selecting a six or three. ​(b) Compute the probability of randomly selecting a six or three or ace. ​(c) Compute the probability of randomly selecting a three or diamond.

(a) 0.154 (b) 0.231 (c) 0.308

A probability experiment is conducted in which the sample space of the experiment is S={8,9,10,11,12,13,14,15,16,17,18,19}. Let event E={10,11,12,13}. Assume each outcome is equally likely. List the outcomes in Ec. Find PEc.

(a) Ec={8,9,14,15,16,17,18,19} (b) P(Ec)= 0.667

A probability experiment is conducted in which the sample space of the experiment is S={9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}​, event F={12, 13, 14, 15, 16}​, and event G={16, 17, 18, 19}. Assume that each outcome is equally likely. (a) List the outcomes in F or G. (b) Find P(F or G) by counting the number of outcomes in F or G. (c) Determine P(F or G) using the general addition rule.

(a) F or G= {12,13,14,15,16,17,18,19} (b) Outcomes in F or G= 0.667 (c)

A probability experiment is conducted in which the sample space of the experiment is S={5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}​, event F={6, 7, 8, 9, 10, 11}​, and event G={10, 11, 12, 13}. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule. (a) List the outcomes in F or G. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. (b) Find P(F or G) by counting the number of outcomes in F or G. (c) Determine P(F or G) using the general addition rule. Select the correct choice below and fill in any answer boxes within your choice.

(a) F or G= {6,7,8,9,10,11,12,14} (b) P(E or F)=P(E)+P(F)−P(E and F).... =0.667 (c)

The data in the following table show the association between cigar smoking and death from cancer for 140,838 men.​ Note: current cigar smoker means cigar smoker at time of death. LOADING... Click the icon to view the table. (a) If an individual is randomly selected from this​ study, what is the probability that he died from​ cancer? (b) If an individual is randomly selected from this​ study, what is the probability that he was a current cigar​ smoker? (c) If an individual is randomly selected from this​ study, what is the probability that he died from cancer and was a current cigar​ smoker? (d) If an individual is randomly selected from this​ study, what is the probability that he died from cancer or was a current cigar​ smoker?

(a) P(died from ​cancer)=. 007 ​(b) P(current cigar ​smoker)=. 066 (c) P(died from cancer and current cigar ​smoker)=0.001 ​(d) P(died from cancer or current cigar ​smoker)=. 072

A probability experiment is conducted in which the sample space of the experiment is S={9,10,11,12,13,14,15,16,17,18,19,20}. Let event E={10,11,12,13,14,15} and event F={14,15,16,17}. List the outcomes in E and F. Are E and F mutually​ exclusive?

(a) common outcomes {14,15} (b) No. E and F have common outcomes

The General Addition Rule

For any two events E and F, P(E or F)=P(E)+P(F)−P(E and F)

Addition Rule for Disjoint Events

If E and F are disjoint (or mutually exclusive) events, then P(E or F) = P(E) + P(F)

Complement Rule

If E represents any event and EC represents the complement of E, then P(Ec)=1−P(E)

Idea of compliments

Let S denote the sample space of a probability experiment and let E denote an event. The complement of E, denoted EC, is all outcomes in the sample space S that are not outcomes in the event E. Because E and EC are mutually exclusive, P(E or Ec)=P(E)+P(Ec)=P(S)=1 Subtracting P(E) from both sides, we obtain the following result.

Benford's Law

Mathematical algorithm that accurately predicts that, for many data sets, the first digit of each group of numbers in a random sample will begin with 1 more than a 2, a 2 more than a 3, a 3 more than a 4, and so on. Predicts the percentage of time each digit will appear in a sequence of numbers.

Venn diagrams

These pictures represent events as circles enclosed in a rectangle. the rectangle represents the sample space, and each circle represents an event

Disijointed events

Two events are disjoint if they have no outcomes in common. Another name is mutually exclusive