# Competency Evaluation on Understanding Probability of Two Events

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: A and B are mutually exclusive. Look at the picture, Events A and B never occur at the same time.
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 A∪B=A+B-(A∩B)
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 From a set of cards, two cards are withdrawn one by one without replacement.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.

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