Multiple Choice Exercise

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2.1 If two events A and B are mutually exclusive, what is the probability of the event \(A \cap B\)?

P(A)－P(B)
P(A)P(B)
P(A)＋P(B)
P(A)/P(B)

        

2.2 Let the probability of the event A be P(A) and of the event B be P(B). Which of the followings is not right?

0≤P(A)≤1
-1≤P(B)≤0
P(A∪B)=P(A)+P(B)-P(A∩B)
P(A∩B)=P(A)․P(B|A)

        

2.3 If P(A)=0.4, P(B)=0.2 and P(A｜B)=0.6, What is P(A∩B)?

0.08
0.12
0.24
0.48

        

2.4 When A⊂B, compare the conditional probabilit P(A｜B) with P(A)?

the same or large
small
the same or small
cannot be comparable

        

2.5 When two dices are rolled simultaneously, what is the probability that 2 dots and 5 dots appear simultaneously?

\(\frac{1}{3}\)
\(\frac{1}{6}\)
\(\frac{1}{12}\)
\(\frac{1}{18}\)

        

2.6 When we roll a dice three times, what is the probability that the first, the second, and the third will come out with 5 dots, 3 dots and even number of dots?

\(\frac{1}{30}\)
\(\frac{1}{72}\)
\(\frac{1}{108}\)
\(\frac{1}{276}\)

        

2.7 If you randomly select three bulbs one by one without replacement from a container containing five good bulbs and two defective bulbs, find the probability that one of them is defective?

\(\frac{1}{7}\)
\(\frac{2}{7}\)
\(\frac{3}{7}\)
\(\frac{4}{7}\)

        

2.8 If P(A)=0.4, P(B)=0.2 and P(A｜B)=0.6, what is P(A∩B)?

0.08
0.12
0.24
0.48

        

2.9 P(A)=0.4, P(B)=0.2 and P(A｜B)=0.6, what is P(B｜A)?

0.08
0.24
0.30
0.40

        

2.10 Denote the number of dots when we roll two dices as \((x_1 , x_2 )\) and consider an event B = {\((x_1 , x_2 ) : x_1 > x_2 \) }. What is the probability P(B)?

\(\frac{1}{3}\)
\(\frac{1}{12}\)
\(\frac{5}{12}\)
\(\frac{1}{36}\)

        

2.11 Denote the number of dots when we roll two dices as \((x_1 , x_2 )\) and consider two events A = {\((x_1 , x_2 ) : x_1 + x_2 = 10 \) }, B = {\((x_1 , x_2 ) : x_1 > x_2 \) }. What is the probability P(B｜A)?

\(\frac{1}{3}\)
\(\frac{1}{12}\)
\(\frac{5}{12}\)
\(\frac{1}{2}\)