**Competency Evaluation on Understanding**

Intructions: Choose the one correct answer.

1. If Ᾱ states the complement event of A then *P*(Ᾱ)=⋯

A. 1 D. *P*(A)

B. 1-*P*(A) E. Not necessary

C. 1∙*P*(A)

Correct: B, the explanation:

*P*(Ᾱ)=1-

*P*(A)

2. If the probability of event A=0.3 then the probability of the complement event A=⋯

A. 0.3 B. 0.4 C. 0.5 D. 0.6 E. 0.7

Correct: E, the explanation:

*P*(Ᾱ)=1-

*P*(A)

*P*(Ᾱ)=1-0.3=0.7

3. If A dan B are two mutually exclusive events then the probability of A and B occur at the same time is *P*(A∩B)=⋯

A. 1 D. 0

B. *P*(A)∙*P*(B) E. ½

C. (*P*(A)∙)/*P*(B)

Correct: D, the explanation:

*P*(A∩B)=0

4. If *P*(A∩B)=*P*(A)∙*P*(B) then A and B is called the two events which are …

A. independent D. influenced

B. dependent E. bound

C. freelance

Correct: A, the explanation:

If both events A and B are impossible to occur at the same time then A and B are freelance, *P*(A∩B)=0.

If *P*(A∩B)=*P*(A)∙*P*(B)≠0 then both events A and B are independent or not influenced by each other.

If *P*(A∩B)=*P*(A)∙*P*(B|A) then event B is dependent under event A. In other words, event B does not occur, if A didn’t.

5. If A and B are two events that can occur at the same time, then *P*(A∪B)=⋯

A. *P*(A)+*P*(B)-*P*(A∩B)

B. *P*(A)+*P*(B)

C. *P*(A)∙*P*(B)

D. 1-[*P*(A)+*P*(B)]

E. *P*(A)+*P*(B)+*P*(A∩B)

Correct: A, the explanation:

The chance of event A and B accur at the same time is given by *P*(A∩B).

The chance of event A or B occurrence is given by *P*(A∪B).

These statements are shown by this picture

*P*(A∪B)=

*P*(A)+

*P*(B)-

*P*(A∩B)

6. If events A and B can occur at the same time where *P*(A)=0.6;*P*(B)=0.75 and *P*(A∩B)=0.43 then *P*(A∪B)=⋯

A. 0.98 B. 0.96 C. 0.94 D. 0.92 E. 0.90

Correct: D, the explanation:

*P*(A∪B)=

*P*(A)+

*P*(B)-

*P*(A∩B)

*P*(A∪B)=0.6+0.75-0.43=0.92

7. Suppose A and B are two events that are not influenced each other, and known that *P*(A)=½;*P*(B)=¼ then *P*(A∩B)=⋯

A. ⅛ B. ⅙ C. ⅕ D. ¼ E. ¾

Correct: A, the explanation:

*P*(A∩B)=

*P*(A)∙

*P*(B)

*P*(A∩B)=½∙¼=⅛

8. If the occurence of the event B depends on the occurence of event A then event B leads to its conditional probability which is denoted by …

A. *P*(A|B) C. *P*(A,B) E. *P*(A∪B)

B. *P*(B|A) D. *P*(A∩B)

Correct: B, the explanation:

Its meaning.

9. From a set of cards, two cards are withdrawn one by one without replacement. If the first withdrawal is an ace, then the probability of the king is on the second withdrawal =⋯

A. 4/52 B. 3/52 C. 4/51 D. 3/51 E. 13/51

Correct: D, the explanation:

Suppose the set of cards contains 52 cards. It consist of 4 types. Each type has plenty of cards as many as other and has similar characters, e.g: ace, king, queen, jack and numbers.

Hence the chance of drawing an ace is equal to the chance of drawing a king with replacement.

*P*=4/52=1/13

Remember term Conditional Probability.

Thus the chance of drawing a king after an ace had been drawn without replacement is equal to

10. Event A is called independent on event B, if …

A. the occurence of event A depends on the event B

B. the occurence of event A does not depend on the event C. A and B affect each other

D. the occurence of the event B depends on event A

E. event A does not occur even if B has occured

Correct: B, the explanation:

Clear.