Arithmatical Probability
DIRECTIONS : Problems based on Probability.
1. 
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? 

A. 1/10 

B. 2/5 

C. 2/7 

D. 5/7 
Solution 
P(getting a prize)  = 10 / (10+25) 
‹=› 10 / 35 
‹=› 2 / 7. 

2. 
A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? 

A. 3/4 

B. 4/7 

C. 1/8 

D. 3/7 
Solution 
Total number of balls  =(6+8) 
= 14. 
Number of white balls  = 8. 
P(drawing a white ball)  = 8/14 
‹=› 4/7. 

3. 
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings? 

A. 1/15 

B. 25/57 

C. 35/256 

D. 1/221 
Solution 
Let S be the sample space. Then, 
n(S) = ^{52}C_{2}  = (52×51)/(2×1) 
= 1326. 
Let E = event of getting 2 kings out of 4. 
n(E) = ^{4}C_{2}  = (4×4)/(2×1) 
= 6. 
P(E) = n(E) / n(S)  = 6 / 1326 
= 1/221. 

4. 
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability taht the ticket drawn has a number which is a multiple of 3 or 5? 

A. 1/2 

B. 2/5 

C. 8/15 

D. 9/20 
Solution 
Here S=(1,2,3,4,5,...,19,20). 
Let E=event of getting a multiple of 3 or 5 
= (3,6,9,12,15,18,5,10,20) 
P(E)= n(E) / n(S) 
= 9/20. 

5. 
What is the probability of getting a sum 9 from two throws of a dice? 

A. 1/6 

B. 1/8 

C. 1/9 

D. 1/12 
Solution 
In two throws of a die, n(S) = (6×6) 
= 36. 
Let E = event of getting a sum 9= {{3,6),(4,5),(5,4),(6,3)} 
P(E)  = n(E) / n(S) 
= 4/36 
‹=›1/9. 
