Probability -Aptitude

21.

An unbiased die is thrown twice. Let the event A be ‘odd number on the first throw’ and B the event  ‘odd number on the second throw’. Check the independence of the events A and B. 

   A.) A or B are independent events
   B.) A and B are not independent events
   C.) A and B are independent events
   D.) None of these

Answer: Option 'C'

If all the 36 elementary events of the experiment are considered to be equally likely, we have
P(A) = 18/36 = 1/2 
= and P(B) = 18/36 = 1/2 
Also P(A n B) = P (odd number on both throws)
= 9/36 = 1/4 
Now P(A) P(B) = 1/2 × 1/2 = 1/4 
P(A n B) = P(A) × P(B) 
A and B are independent events

22.

Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number? 

   A.) 2/7
   B.) 6/7
   C.) 7/2
   D.) 4/7

Answer: Option 'D'

Let A be the event ‘the number on the card drawn is even’ and B be the 
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B). 
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10} 
and A n B = {4, 6, 8, 10} 
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10 
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7

23.

If P(A) = 6/17, P(B) = 5/17, and P(A ∪ B) = 4/17 Find P(B|A)? 

   A.) 6/3
   B.) 2/5
   C.) 2/7
   D.) 2/3

Answer: Option 'D'

P(B|A) = P(A ∪ B)/P(A) 
P(B|A) = (4/17)/(6/17) = 4/6 = 2/3.

24.

If P(A) = 5/13, P(B) = 7/13, and P(A ∩ B) = 8/13, Find P(A ∪ B)? 

   A.) 4/13
   B.) 5/13
   C.) 6/13
   D.) None of these

Answer: Option 'A'

P(A ∩ B) = P(A) + P(B) - P(A ∪ B) 
= 8/13 = 5/13 + 7/13 - P(A ∪ B) 
= P(A ∪ B) = 5/13 + 7/13 - 8/13 
= P(A ∪ B) = 4/13.


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