A number is selected from the set {1,2,3,...,20}. The probability that the selected number is divisible by 3 or 4 is

(a)

\({2\over5}\)

(b)

\({1\over8}\)

(c)

\({1\over2}\)

(d)

\({2\over3}\)

A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are\({3\over4},{1\over2},{5\over 8}\). The probability that the target is hit by A or B but not by C is

(a)

\({21\over64}\)

(b)

\({7\over32}\)

(c)

\({9\over64}\)

(d)

\({7\over8}\)

If A and B are any two events, then the probability that exactly one of them occur is

(a)

\(P(A\cup\overline{B})+P(\overline{A}\cup B)\)

(b)

\(P(A\cap\overline{B})+P(\overline{A}\cap B)\)

(c)

\(P(A)+P({B})-P({A}\cap B)\)

(d)

\(P(A)+P({B})+2P({A}\cap B)\)

Let A and B be two events such that \(P(\overline{A\cup B})={1\over6}, P(A\cap B)={1\over4}\) and \({P(\overline{A})}={1\over4}\). Then the events A and B are

(a)

Equally likely but not independent

(b)

Independent but not equally likely

(c)

Independent and equally likely

(d)

Mutually inclusive and dependent

Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective

(a)

\({19\over 33}\)

(b)

\({17\over 33}\)

(c)

\({23\over 33}\)

(d)

\({13\over 33}\)

A man has 3 fifty rupee notes, 4 hundred rupees notes, and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?

(a)

1:12

(b)

12:1

(c)

13:1

(d)

1:13

A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is

(a)

\({7\over 45}\)

(b)

\({17\over 90}\)

(c)

\({29\over 90}\)

(d)

\({19\over 90}\)

A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

(a)

\({3\over 16}\)

(b)

\({3\over 8}\)

(c)

\({1\over 4}\)

(d)

\({5\over 8}\)

A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is

(a)

\({3\over 14}\)

(b)

\({5\over 14}\)

(c)

\({1\over 14}\)

(d)

\({9\over 14}\)

If A and B are two events such that A ⊂ B and P(B)\(\neq o\), then which of the following is correct?

(a)

\(P(A/B)={P(A)\over P(B)}\)

(b)

P(A/B)

(c)

P(A/B)\(\ge\)P(A)

(d)

P(A/B)>P(B)