RRB NTPC - Probability -Aptitude

1.

What is the probability that when a hand of 5 cards is drawn from a well shuffled deck of 52 cards,

   A.) 192/37015
   B.) 182/379015
   C.) 192/37901
   D.) 192/379015

Answer: Option 'D'

nCr = n!/(n-r)!r! 
Total number of possible hands = 52C5
52C5 = 2274090 
Number of hands with 4 Queens = 4C4 × 48C1 
4C4 = 24 
4C1 = 48 
(other 1 card must be chosen from the rest 48 cards) 
Hence P (a hand will have 4 Queens) = (4C4 × 48C1)/52C5 = 192/379015.

2.

Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace?

   A.) 2/5530
   B.) 3/5525
   C.) 2/5525
   D.) 4/5525

Answer: Option 'C'

Let Q denote the event that the card drawn is queen and A be the event that 
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52 
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51 
P(A|QQ) is the probability of third drawn card to be an ace, with the condition 
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50 
By multiplication law of probability, we have 
P(QQA) = P(Q) P(Q|Q) P(A|QQ) 
= 4/52 × 3/51 × 4/50 
= 2/5525.

3.

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.

4.

6 Coins are tossed simultaneously. find the probability to get 2 hands 

   A.) 15/32
   B.) 5/64
   C.) 15/64
   D.) None of these

Answer: Option 'C'

26 = 64, ( 1 = 2, 2 = 4, 4 = 16, 16 = 32, 32=64 times ) 
6c2 = 6!/2! = (6 × 5 × 4 × 3 × 2 × 1)/ (6 - 2)! × (2 × 1) = 15
Probability = 15/64.

5.

A die is thrown. If G is the event 'the number appearing is a multiple of 3' and H be the event 'the number appearing is even' then find whether G and H are independent ? 

   A.) G and H are not independent events.
   B.) G and H are independent events.
   C.) Only G independent event
   D.) None of these

Answer: Option 'B'

We know that the sample space is S = {1, 2, 3, 4, 5, 6}
Now G = { 3, 6}, F = { 2, 4, 6} and E n F = {6}
Then P(G) = 2/6 = 1/3 
P(H) = 3/6 = 1/2 and P(G ∩ H) = 1/6 
P(G n H) = P(G). P (H) 
G and H are independent events.

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