RRB NTPC - Probability -Aptitude

1.

If P(A) = 2/15, P(B) = 4/15, and P(A ∪ B) = 6/15 Find P(A|B) 

   A.) 6/15
   B.) 3/4
   C.) 3/2
   D.) None of these

Answer: Option 'C'

P(A|B) = P(A ∪ B)/P(B) 
P(A|B) = (6/15)/(4/15) = 3/2.

2.

If P (A) = 0.18, P (B) = 0.5 and P (B|A) = 0.2, find P(A n B)? 

   A.) 0.32
   B.) 0.36
   C.) 0.16
   D.) 0.64

Answer: Option 'B'

P(B|A) = P(A n B)/P(A) 
P(A n B) = P(B|A) × P(A) 
P(A n B) = 0.2 × 0.18 
P(A n B) = 0.36

3.

Let A and B be independent events with P (A) = 0.2 and P(B) = 0.8. Find P(A/B)? 

   A.) 0.2
   B.) 0.3
   C.) 1.2
   D.) None of these

Answer: Option 'A'

P(A/B) = P (A n B)/P(B) 
Here, P (A n B) = 0.16 
P(A/B) = 0.16/0.8 = 0.2

4.

Events A and B are such that P (A) = 1/3, P(B) = 7/6, and P(not A or not B) = 1/4. State whether A and B are independent? 

   A.) A and B are independent
   B.) A and B are not independent
   C.) A and B are neither or not independent
   D.) None of these

Answer: Option 'B'

P(A) = 1/3, P(B) = 7/6 
Also P(A n B) = P 
P(A n B) = 1/4 
Now P(A) P(B) = 1/3 × 7/6 = 7/18 
But P(A n B) = 1/4 
Clearly P(A n B) ≠ P(A) × P(B) 
Thus, A and B are not independent events

5.

If A and B are two events such that P (A) = 3/4, P (B) = 1/2 and P (A n B) = 3/8, find P (not A and not B). 

   A.) 3/8
   B.) 1/8
   C.) 1/4
   D.) None of these

Answer: Option 'B'

P(not A and not B) = 1 - (P(A) + P(B) - P(AB)) 
which you might find somewhere in your text.
Substituting in our probabilities we get: 
P(not A and not B) = 1 - (3/4 + 1/2 - 3/8) 
P(not A and not B) = 1 - (7/8) 
P(not A and not B) = 1/8.

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