Probability  Aptitude basics, practice questions, answers and explanations

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Probability of an event= (No of occurrences of an event)/(Total no. of possible outcomes)

P(E) = n(E)/n(U)
where n(E)= no. of occurrences of event; n(U)= total possible outcomes

Probability of head in a toss=1/2
Probability of tails in a toss=1/2
Probability of any side in a throw of dice=1/6
Probability of getting a sign in a deck of cards= 1/4
Probability of getting an ace; king; queen etc= 1/13
Probability of occurrence of 2 independent events= P(A)*P(B)

Exercise Questions

1. If 10 letters are to be placed in 10 addressed envelopes, then what is the probability that at least one letter is placed in wrong addressed envelope?
a.1/10!    
b.1/9!     
c.1- (1/10!)           
d.9/10

2.Two letters are selected randomly from English alphabet simultaneously. What is the probability that one is a constant and the other a vowel?
a.10/67      
b.21/65    
c.44/65    
d.2/13

3. Two dice are rolled together. The probability that the sum of the numbers shown on the two dice is maximum or minimum is……
a.1/18          
b.1/9      
c.1/6       
d.1/36

4. A bag has 5 red balls and 3 green balls and another bag contains 4 green balls and 3 red balls. If one ball is drawn from each bag, then what is the probability that both are green balls?
a.5/14          
b.3/14          
c.11/14    
d.9/14

5. Two cards are drawn at random from a pack of cards. The probability that both are queens or diamonds is……
a.20/221    
b.15/221    
c.13/221    
d.14/221

6. If a coin is tossed 6 times, then the probability of getting exactly 1 head is ………..
a.1/32          
b.13/32    
c.5/32          
d.3/32

7. Amit throws a biased coin on which the head appears in 65% of the situations. In a game involving this coin, if Amit is paid Rs.15 per head and he has to pay Rs.20 for a tail, then in the long run, per game Amit makes an average……
a.Profit of Rs.2.25    
b.loss of Rs.2.25    
c.profit of Rs.2.75    
d.loss of Rs.2.75

8. From a box containing a dozen bulbs, of which exactly one half are good, and four bulbs are chosen at random to fit into the four bulb holders in a room. The probability that the room gets lighted is…………
a.2/3      
b.1/3      
c.33/44    
d. 32/33

9. From a bag containing 6 pink and 8 orange balls, 8 balls are drawn at random. The probability that 5 of them are pink and the rest are orange is…………
a.16/143    
b.19/143    
c.17/143    
d. 13/143

10. A bag contains 5 five-rupee coins, 8 two-rupee coins and 7 one-rupee coins. If four coins are drawn from the bag at random, then find the odds in favour of the draw yielding the maximum possible amount.
a.1:968
b.968:969          
c.1:969
d.969:968

Answer Key

1.c; 2.b; 3.a; 4.b; 5.d; 6.d; 7.c; 8.d; 9.a; 10.a