Probability - aptitude test

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1) Three unbiased coins are tossed. What is the probability of getting at least 2 tails?

a) 0.75
b) 0.5
c) 0.25
d) 0.2

Solution :

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
E = {HTT, THT, TTH, TTT}
n(S) = 8
n(E) = 4
P(E) =n(E) / n(S) = 4/8 = 0.5

2) Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?

a) 9/25
b) 9/50
c) 18/25
d) None of these

Solution:

S = {1, 2, 3, … , 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18
P(E) = n(E)/n(S) = 18/50
= 9/25

3) From a pack of 52 cards, one card is drawn at random. Find the probability that the drawn card is a club or a jack?

a) 17/52
b) 8/13
c) 4/13
d) 1/13

Solution:

n(S) = 52
n(E) = 16
P(E) = n(E) / n(S) = 16/ 52
= 4/13

4) Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?

a) 8/35
b) 34/35
c) 27/35
d) None of these

Solution:

P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35