This course is concerned with the basic understanding of probability and it’s applications. The goal is to learn and you get back what you put in. Briefly state the question and use the Equation Editor to present all equations clearly. Answer any 2 questions.

For probability questions, define events as:

A: drawing a 10♣

B: drawing a 9♥

P(A&B) = P(A)P(B|A) = ??

Special Exercises (1to 5)

1. What is the probability of drawing at random the 4♥ and the 9♣ from a deck of cards on two successive draws? Use Insert/Insert symbol to get the heart, club, diamond, spade symbol by selecting the drop down menu to the left of Paragraph. Also, click on the drop down menu next to the Black Square icon in the menu of the Editor to change colors of the characters.

2. 18 people were poled and 10 said they have shopped at Wal-Mart and 8 said they have shopped at Target. 4 said they shopped at both. What is the probability that the group shopped at Wal-Mart or Target?.

3. Define independent and mutually exclusive events mathematically by using P(A) & P(B) for events A & B.

4. What is the probability of randomly drawing a 10 or a ♦ from a deck of cards?

5. What are the total possible outcomes of rolling a pair of dice? Note that the pair 3,4 is not the same as the pair 4,3. What is the probability of rolling a 7 with a pair of dice? P(7) = No. of successful outcomes/Total No. of outcomes

In questions 1,2,4, begin by clearly defining events A & B as shown below.

For example, A: 4♥ and B: 9♣. State P(A)=??, P(B)=?? and then apply the appropriate equations , such as

P(A&B) = P(A)P(B|A) or P(AorB) = P(A)+P(B)-P(A&B)

Substitute values and compute the answer. I urge you to read the attachments in the Videos-Topics In Stat 230/Probability Rules.

I prefer to use P(A&B) or P(AorB) instead of P(A∩B) or P(A∪B). You will see the latter on the final so be sure you know what the “∩” and “U” symbols mean.

COMPLEMENTARY EVENTS & Try It 3.19 in Illowsky

Complement_&_Rule.swf

The complement of an event A is the event A does not occur. The complement of event A is denoted by Ac and either event A or Ac must occur. Therefore,

P(A) + P(Ac) = 1.0

or,

P(A) = 1.0 – P(Ac)

For example, consider tossing a fair coin 10 times. Define event A as;

A: Observe at least one head

Ac: TTTTTTTTTT (observe no heads, 10 tails are tossed)

P(Ac) = (12)10=11024

P(A) = 1.0 − P(Ac) =1−11024=.999

We are fairly sure of observing at least one head in ten tosses.

Dependent vs Independent Events

Independent Events: Consider tossing two die. What is the probability of throwing a “One” on die #1 and then a “Six” on die # 2? Answer is 1/6 times 1/6 = 1/36. These events are independent of each other and P(A&B) = P(A)P(B).

Dependent events: What is the probability of drawing the Queen of Spades and the King of Spades if no card is repaced after the first draw. We apply the rule that P(A&B) = P(A)P(B|A) = P(B)P(A|B). Since A is the queen, P(A) = 1/52 and to then draw the kink, P(B|A) = 1/51, the answer is 1/52 times 1/51. Recall that P(B|A) means the probability that event B occurs given that event A has already occurred. Event B is dependent upon event A occurring.

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