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There is a five-volume dictionary among 50 books arranged on a shelf in random order. If the volumes are not necessarily kept side by side, the probability that they occur in increasing order from left to right is

(a) 1/5! (b) 1/550 (c) 1/505 (d) None of these Solution: The total number of arrangement of 50 books =... View Article

A bag contains 50 tickets numbered 1, 2, 3, …., 50 of which five are drawn at random and arranged in ascending order of magnitude (x₁ < x₂ < x₃ < x₄ < x₅). The probability that x₃ = 30 is

(a) 20C2/ 50C5 (b) 2C2/ 50C5 (c) 20C2 ×29C2/ 50C5 (d) none of these Solution: The number of ways of... View Article

From past experience it is known that an investor will invest in security A with a probability of 0.6, will invest in security B with a probability 0.3 and will invest in both A and B with a probability of 0.2. What is the probability that an investor will invest neither in A nor in B?

(a) 0.7 (b) 0.28 (c) 0.3 (d) 0.4 Solution: Given P(A) = 0.6 P(B) = 0.3 P(A⋂B) = 0.2 P(A⋃B)... View Article

If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25?

(a) 0 (b) 1/2 (c) 1 (d) 1/1296 Solution: Maximum value on a die = 6 When 4 dice are... View Article

Three digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8, and 9 without repeating any digit. What is the probability that the product is odd?

(a) 2/3 (b) 7/48 (c) 5/42 (d) 5/108 Solution: Total number of 3-digit numbers = 9 ×8 ×7 = 504... View Article

A box contains 10 identical electronic components of which 4 are defective. If 3 components are selected at random from the box in succession, without replacing the units already drawn, what is the probability that two of the selected components are defective?

(a) 1/5 (b) 5/24 (c) 3/10 (d) 1/40 Solution: Total number of ways of selecting 3 components out of 10... View Article

Let A, B, C be three events. If the probability of occurring exactly one event out of A and B is 1-a, out of B and C and A is 1-a and that of occurring three events simultaneously is a², then the probability that at least one out of A, B, C will occur is

(a) 1/2 (b) Greater than 1/2 (c) Less than 1/2 (d) Greater than 3/4 Solution: P (exactly one event out... View Article

An aircraft has three engines A, B, and C. The aircraft crashes if all three engines fail. The probabilities of failure are 0.03, 0.02, and 0.05 for engines A, B, and C respectively. What is the probability that the aircraft will not crash?

(a) 0.00003 (b) 0.90 (c) 0.99997 (d) 0.90307 Solution: Let P(A), P(B) and P(C) denotes the probabilities of failure of... View Article

Two numbers are successively drawn from the set U = {1, 2, 3, 4, 5, 6, 7, 8}, the second being drawn without replacing the first. The number of elementary events in the sample is:

(a) 64 (b) 56 (c) 32 (d) 14 Solution: U = {1, 2, 3, 4, 5, 6, 7, 8} n(U)... View Article

A machine has three parts, A, B, and C, whose chances of being defective are 0.02, 0.10, and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?

(a) 0.06 (b) 0.16 (c) 0.84 (d) 0.94 Solution: Let P(A), P(B), P(C) be the probability of parts A, B... View Article

x₁, x₂, x₃, ……., x₅₀ are fifty real numbers such that x_r <x_r+1 for r = 1, 2, 3, …., 49. Five numbers out of these are picked up at random. The probability that the five numbers have x₂₀ as the middle number, is

(a) 20C2 ×30C2/50C5 (b) 30C2 ×19C2/50C5 (c) 19C2 ×31C3/50C5 (d) none of these Solution: n(S) = 50C5 n(E) = 30C2... View Article

If n objects are distributed at random among n persons, the probability that at least one of them will not get anything is

(a) 1 – (n-1)!/nn-1 (b) (n-1)!/nn (c) 1 – (n-1)!/nn (d) none of these Solution: The first object can be... View Article

A car is parked by an owner amongst 25 cars in a row, not at either end. On his return, he finds that exactly 15 places are still occupied. The probability that both the neighboring places are empty is

(a) 91/276 (b) 15/184 (c) 15/92 (d) none of these Solution: Since only 15 places are occupied, 10 cars have... View Article

What is the number of outcomes when a coin is tossed and then a die is rolled only in case a head is shown on the coin?

(a) 6 (b) 7 (c) 8 (d) None of these Solution: When a coin is tossed, if we get a... View Article

A coin is tossed three times. Consider the following events:

A: No head appears B: Exactly one head appears C: At least two heads appear Which one of the following... View Article

If A, B, C are events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A ⋂ B) = 0.08, P(A ⋂ C) = 0.28, P(A ⋂ B ⋂ C) = 0.09. If P(A ⋃ B ⋃ C) ≥ 0.75, then find the range of x = P(B ⋂ C) lies in the interval

(a) 0.23 ≤ x ≤ 0.48 (b) 0.23 ≤ x ≤ 0.47 (c) 0.22 ≤ x ≤ 0.48 (d) None... View Article

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is

(a) 1/3 (b) 1/5 (c) 1/10 (d) 1/2 Solution: Total number of triangles formed = 6C3 = 20 The only... View Article

A certain type of missile hits the target with a probability of p = 0.3. What is the least number of missiles that should be fired so that there is at least an 80% probability that the target is hit?

(a) 5 (b) 6 (c) 7 (d) None of the above Solution: Let P(a) = 0.3 = 3/10 If ‘n’... View Article

In a series of 3 one-day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively. If a win, loss or draw gives 2, 0 and 1 point respectively, then what is the probability that team A will score 5 points in the series?

(a) 17/18 (b) 11/12 (c) 1/12 (d) 1/18 Solution: To score 5 points, team A needs to win 2 matches... View Article

In a knock-out chess tournament, eight players P₁, P₂, …P₈ participated. It is known that whenever the players P_i and P_j play, the players P_i will win j if i < j. Assuming that the players are paired at random in each round, what is the probability that the player P₄ reaches the final?

(a) 31/35 (b) 4/35 (c) 8/35 (d) None of these Solution: Let us divide the players into two pools A... View Article

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