A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies\({(x-10)(x-50)\over x-30}\ge0\), then P(A) is

(a)

0.20

(b)

0.51

(c)

0.71

(d)

0.70

If two events A and B are independent such that P(A) = 0.35 and \(P(A\cup B)=0.6\), then P(B) is

(a)

\({5\over 13}\)

(b)

\({1\over 13}\)

(c)

\({4\over 13}\)

(d)

\({7\over 13}\)

If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then \(P(\overline{A}\cap B )\) is

(a)

0.96

(b)

0.24

(c)

0.56

(d)

0.66

There are three events A, B, and C of which one and only one can happen. If the odds are 7 to 4 against A and 5 to 3 against B, then odds against C is

(a)

23: 65

(b)

65: 23

(c)

23: 88

(d)

88: 23

If a and b are chosen randomly from the set {1,2,3,4} with replacement, then the probability of the real roots of the equation \(x^2+ax+b=0\) is

(a)

\({3\over 16}\)

(b)

\({5\over 16}\)

(c)

\({7\over 16}\)

(d)

\({11\over 16}\)

It is given that the events A and B are such that \(P(A)={1\over4},P(A/B)={1\over2}\) and \(P(B/A)={2\over3}.\) Then P(B) is

(a)

\({1\over 6}\)

(b)

\({1\over 3}\)

(c)

\({2\over 3}\)

(d)

\({1\over 2}\)

In a certain college 4% of the boys and 1% of the girls are taller than 1.8 meter. Further 60% of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is

(a)

\({2\over 11}\)

(b)

\({3\over 11}\)

(c)

\({5\over 11}\)

(d)

\({7\over 11}\)

Ten coins are tossed. The probability of getting at least 8 heads is

(a)

\(7\over 64\)

(b)

\(7\over 32\)

(c)

\(7\over 16\)

(d)

\(7\over 128\)

The probability of two events A and B are 0.3 and 0.6 respectively. The probability that both A and B occur simultaneously is 0.18. The probability that neither A nor B occurs is

(a)

0.1

(b)

0.72

(c)

0.42

(d)

0.28

If m is a number such that m \(\le\) 5, then the probability that quadratic equation 2x² + 2mx + m + 1 = 0 has real roots is

(a)

\({1\over 5}\)

(b)

\({2\over 5}\)

(c)

\({3\over 5}\)

(d)

\({4\over 5}\)