Mike's pencil box contains 30 pens. 15 of the pens are red, and all of

Question

Mike's pencil box contains 30 pens. 15 of the pens are red, and all of the others are either blue or black. If Mike were to choose a random pen from the pencil box, what is the probability that it would be blue?

(1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3
(2) The probability that the pen will be red or blue is 0.8

chetan2u · Answer

Total pens: 30
Red pens: 15
Blue or Black: 15.....If Blue are b in number, then Blacks are 15-b

We have to find P(blue) or  \frac{b}{30}

(1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3

P(Red) =  \frac{15}{30} , and P(Black) =  \frac{15-b}{30}

Thus  \frac{15}{30}-\frac{15-b}{30}=0.3=\frac{3}{10}

\frac{b}{30}=\frac{9}{30}....b=9

\frac{b}{30}=\frac{9}{30}=0.3

Sufficient

(2) The probability that the pen will be red or blue is 0.8

So probability that it is black is 1-0.8=0.2.

P(Black) =  \frac{15-b}{30}=0.2...15-b=6....b=9

Thus, P(Blue)= \frac{b}{30}=\frac{9}{30}=0.3

Sufficient

D

sumitkrocks · Answer

We know 
P_Red = 15/ 30 = 1/2 = 0.5

Statement 1: The probability that the pen will be red minus the probability that the pen will be black equals 0.3
P_Red - P_Black = 0.3
0.5 - P_Black =0.2
P_Black = 0.3
Also, P_Red + P_Black + P_Blue = 1
P_Blue = 1-0.5-0.3 = 0.2
Sufficient

Statement 2: The probability that the pen will be red or blue is 0.8
Since the events are mutually exclusive 
The probability that the pen will be red or blue =P_Red + P_Blue = 0.8 
P_Blue = 0.8 - 0.5 = 0.3 
Sufficient

D is the answer IMO

ArindamLucky · Answer

IMO D

(1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3

P(R) =15/30
P(BLUE) =B/15
P(BLACK) =BL/15   --- 1

As per statement 
P(R) - P(BLACK) =15 - BL/30 =0.3

Solving you will get all the values, Sufficient

(2) The probability that the pen will be red or blue is 0.8

P(R) + P(B)/30 = 0.8
put values from 1 and you will get the values, Sufficient

Mike's pencil box contains 30 pens. 15 of the pens are red, and all of

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