Probability Questions Quiz for Canara Bank PO, IBPS Clerk, SBI Clerk, Syndicate Bank PO

Probability Questions Quiz for IBPS Clerk Mains, Syndicate Bank PO and Canara Bank PO

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Directions: Study the following information carefully and answer the questions given beside:

1
Directions (Set of 2 Questions): Kindly study the following information carefully and answer the question that follows:

A shop sells 10 tube lights out of which 3 are defective. Salman buys four tube lights.
 
Find the probability that at least two of the tube lights that he buys work.
» Explain it
A
Following the common explanation, we get

Probability that at least two of Salman's tube lights work 

=   29
30

Hence, option A is correct.

Common Explanation:

n(S) = 10C4 = 210

7 of the 10 lamps are not defective.

∴   If T is the event that all of Salman's tube lights work,

n(T) = 7C4 = 35

∴   Probability that all of Salman's tube lights work  
=   35  =  1
210 6

We need the probability that at least two of his tube lights work.

The event that less than two of his tube lights work,

and the event that at least two of his tube lights work, are exhaustive.

So, we calculate the probability that less than two of his tube lights work and subtract it from 1.

The probability that none of Salman's tube lights work = 0 as there are only 3 defective tube-lights and he buys 4. If K is the probability that only one of Salman's tube lights works,

n(K) = 7C1 × 3C3 = 7

∴   Probability that less than two of Salman's tube lights work
 
7  =  1
210 30

∴   Probability that at least two of Salman's tube lights work
 
= 1 –  1  =  29
30 30

2
A shop sells 10 tube lights out of which 3 are defective. Salman buys four tube lights.
 
Find the probability that all of Salman’s tube lights work.
» Explain it
E
Following the common explanation, we get

Probability that all of Salman's tube lights work

=   1
6

Hence, option E is correct.

Common Explanation:

n(S) = 10C4 = 210

7 of the 10 lamps are not defective.

∴   If T is the event that all of Salman's tube lights work,

n(T) = 7C4 = 35

∴   Probability that all of Salman's tube lights work

=   35  =  1
210 6

We need the probability that at least two of his tube lights work.

The event that less than two of his tube lights work,

and the event that at least two of his tube lights work, are exhaustive.

So, we calculate the probability that less than two of his tube lights work and subtract it from 1.

The probability that none of Salman's tube lights work = 0 as there are only 3 defective tube-lights and he buys 4. If K is the probability that only one of Salman's tube lights works,

n(K) = 7C1 × 3C3 = 7

∴   Probability that less than two of Salman's tube lights work
 
7  =  1
210 30

∴   Probability that at least two of Salman's tube lights work
 
= 1 –  1  =  29
30 30

3
Directions (Set of 2 Questions): Kindly study the following information carefully and answer the question that follows:

From a box containing 8 yellow and 5 white pens, three are drawn one after the other.
 
Find the probability of all three pens being yellow if the pens drawn are not replaced?
» Explain it
A
If the pens are being drawn one after another, the probability of drawing any color of pens for every fresh draw changes.

∴   Reqd probability =  8  ×  7  ×  6  =  336
13 12 11 1716

Hence, option A is correct.

4
From a box containing 8 yellow and 5 white pens, three are drawn one after the other.

Find the probability of all three pens being yellow if the pen drawn is replaced by another yellow colored pen before the next pen is picked.
» Explain it
B
When the pens drawn are replaced, we can see that the number of pens available for drawing out will be the same for every draw. This means that the probability of a yellow pen appearing in every draw are will be the same.

∴   Reqd probability =  8  ×  8  ×  8  =  512
13 13 13 2197

Hence, option B is correct.

5
Directions (Set of 2 Questions): Kindly study the following information carefully and answer the question that follows:

A box contains 4 white, 6 green, 2 red and 5 yellow pens.
 
If two pens are picked at random, what is the probability that both of them are green?
» Explain it
C
Total number of pens = 4 + 6 + 2 + 5 = 17

∴   n(S) = 17C2 17 × 16  = 136
2

∴   n(E) = 6C2 5 × 6  = 15
1 × 2

∴   Reqd probability =  15
136

Hence, option C is correct.