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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 = 10C3 Number... 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 of A and B... 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 A,... 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) = 8 Number of ways of selecting first... 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 and C working... 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 distributed to any of the n... 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 left. The total... 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 head, we roll a die. When a die is... 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 is correct? (a) (A⋃B) ⋂ (A⋃C) =... 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 of these Solution: P(A ⋃ B ⋃ C) ≥ 0.75... 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 equilateral triangles possible are... 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' is the no. of times that the missile is... 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 and draw 1 match. Let W... 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 and B each containing 4... View Article

Amar, Bimal and Chetan are three contestants for an election, odds against Amar will win is 4 : 1 and odds against Bimal will win is 5 : 1 and odds in favor of Chetan will win 2 : 3 then what is probability that either Amar or Bimal or Chetan will win the election.

(a) 23/20 (b) 11/30 (c) 7/10 (d) None of these Solution: The probability that Amar will win the tournament is P(A) =... View Article

Ravish writes letters to his five friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?

(a) 109 (b) 118 (c) 119 (d) None of these Solution: The number of possible ways of putting 5 letters into 5 envelopes = 5!... View Article

If (2/9!) + (2/3! 7! ) + (1/5!5!) = 2^a/b!, where a, b ∈ N, then the ordered pair (a, b) is

(a) (9, 10) (b) (10, 9) (c) (7, 10) (d) (10, 7) Solution: (2/9!) + (2/3! 7! ) + (1/5!5!) = 2a/b! (1/7!) [... View Article

The horizontal range of an oblique projectile is four times maximum height attained by the projectile. The angle of projection is

The horizontal range of an oblique projectile is four times the maximum height attained by the projectile. The angle of projection is (a) 45... View Article

Two poles of height 6m and 11m stands on a plane ground, if the distance between the feet is 12m. Find the distance between the tops.

Two poles of height 6m and 11m stand on a plane ground if the distance between the feet is 12m. Find the distance between the tops. (a) 12 m (b)... View Article