Total Questions:25 Total Time: 45 Min
Remaining:
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 \(x = \)
\(\frac{3}{{10}}\)
\(\frac{1}{2}\)
\(\frac{2}{5}\)
\(\frac{1}{5}\)
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 \(P(B) = \)
\(\frac{5}{6}\)
\(\frac{5}{7}\)
\(\frac{3}{5}\)
Question:One card is drawn from a pack of 52 cards. The probability that it is a queen or heart is
\(\frac{1}{{26}}\)
\(\frac{3}{{26}}\)
\(\frac{4}{{13}}\)
\(\frac{3}{{13}}\)
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
Independent but not equally likely
Mutually exclusive and independent
Equally likely and mutually exclusive
Equally likely but not independent
Question:If A and B are two independent events such that \(P\,(A) = \frac{1}{2},\,\,P(B) = \frac{1}{5},\) then
\(P\,\left( {\frac{A}{B}} \right) = \frac{1}{2}\)
\(P\,\left( {\frac{A}{{A \cup B}}} \right) = \frac{5}{6}\)
\(P\,\left( {\frac{{A \cap B}}{{A' \cup B'}}} \right) = 0\)
All of the above
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
\(\frac{5}{{14}}\)
\(\frac{5}{{16}}\)
\(\frac{5}{{18}}\)
\(\frac{{25}}{{52}}\)
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
7
6
5
None of these
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
\(\frac{1}{{30}}\)
\(\frac{1}{{10}}\)
\(\frac{1}{3}\)
\(\frac{1}{{15}}\)
Question:In a binomial distribution the probability of getting a success is 1/4 and standard deviation is 3, then its mean is
8
12
10
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
Independent
Mutually exclusive
Dependent
Equally likely