Test on probability

Total Questions:25 Total Time: 45 Min

Remaining:

 

Questions 1 of 25

Question:If \(P\,(A) = 0.4,\,\,P\,(B) = x,\,\,P\,(A \cup B) = 0.7\)and the events A and B are mutually exclusive, then \(x = \)

Answers Choices:

\(\frac{3}{{10}}\)

\(\frac{1}{2}\)

\(\frac{2}{5}\)

\(\frac{1}{5}\)

Questions 2 of 25

Question:Let A and B be two events such that \(P\,(A) = 0.3\) and \(P\,(A \cup B) = 0.8\). If A and B are independent events, then \(P(B) = \)

Answers Choices:

\(\frac{5}{6}\)

\(\frac{5}{7}\)

\(\frac{3}{5}\)

\(\frac{2}{5}\)

Questions 3 of 25

Question:One card is drawn from a pack of 52 cards. The probability that it is a queen or heart is

Answers Choices:

\(\frac{1}{{26}}\)

\(\frac{3}{{26}}\)

\(\frac{4}{{13}}\)

\(\frac{3}{{13}}\)

Questions 4 of 25

Question:Let A and B be two events such that \(P\overline {(A \cup B)} = \frac{1}{6},P(A \cap B) = \frac{1}{4}\) and \(P(\bar A) = \frac{1}{4},\) where \(\bar A\) stands for complement of event A. Then events A and B are

Answers Choices:

Independent but not equally likely

Mutually exclusive and independent

Equally likely and mutually exclusive

Equally likely but not independent

Questions 5 of 25

Question:If A and B are two independent events such that \(P\,(A) = \frac{1}{2},\,\,P(B) = \frac{1}{5},\) then

Answers Choices:

\(P\,\left( {\frac{A}{B}} \right) = \frac{1}{2}\)

\(P\,\left( {\frac{A}{{A \cup B}}} \right) = \frac{5}{6}\)

\(P\,\left( {\frac{{A \cap B}}{{A' \cup B'}}} \right) = 0\)

All of the above

Questions 6 of 25

Question:A bag "A" contains 2 white and 3 red balls and bag "B" contains 4 white and 5 red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag "B" was

Answers Choices:

\(\frac{5}{{14}}\)

\(\frac{5}{{16}}\)

\(\frac{5}{{18}}\)

\(\frac{{25}}{{52}}\)

Questions 7 of 25

Question:At least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is

Answers Choices:

7

6

5

None of these

Questions 8 of 25

Question:The value of C for which \(P\,(X = k) = C{k^2}\) can serve as the probability function of a random variable X that takes 0, 1, 2, 3, 4 is

Answers Choices:

\(\frac{1}{{30}}\)

\(\frac{1}{{10}}\)

\(\frac{1}{3}\)

\(\frac{1}{{15}}\)

Questions 9 of 25

Question:In a binomial distribution the probability of getting a success is 1/4 and standard deviation is 3, then its mean is

Answers Choices:

6

8

12

10

Questions 10 of 25

Question:A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and \(A \cap B = \)card is ace of diamond, then events A and B are

Answers Choices:

Independent

Mutually exclusive

Dependent

Equally likely