Question

A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen?

(a) 1/14 

(b) 2/14 

(c) 3/14 

(d) 4/14

Answer 1

Correct option a (1/14)

Explanation:

Probability of drawing 1 blue pen = 4/9 

Probability of drawing another blue pen = 3/8 

Probability of drawing 1 black pen = 3/7 

Probability of drawing 2 blue pens and 1 black 

pen = 4/9 * 3/8 * 3/7 = 1/14

Comments

How can you sure that first two random pens are blue and 3rd one is black?

First step, first random two pens are blue and not replace and 3rd one is black then probability=4/9*3/8*3/7=1/14

2nd step,for two random Pens first one is black and 2nd one is blue and not replace..then 3rd pen is blue.then probability =3/9*4/8*3/7=1/14

3rd step,for two random pens first one is blue and 2nd one is black and not replace.then 3rd pen is blue.so probability=4/9*3/8*3/7=1/14

So, probability for 2blue pen and 1 black pen=(1/14)+(1/14)+(1/14)=3/14.

From my point of view, answer should be option c(3/14).

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First pen can be black or blue

Similarly,

2nd and 3rd too


So,


3*(4/9)*(3/8)*(3/7)