13. Mohan has a box of coloured pens. He takes a pen at random from the box. The probability that he takes a red pen is 0.4. If the box contains total 50 pens of blue, green and red colours, and there are 15 blue pens and some green pens, then answer the following :
(1) The no of red pen in the box are:
(a) 15
(b) 20
(c) 25
(ii) The probability of taking a green pen is:
(a) 0.6
(b) 0.4
(c) 0.5
(iv) The probability of taking a blue or green pen is
(a) 0.3
(b) 0.4
(c) 0.5
(d) 0.6
Answers
Answer:
1. (b) 20
(ii) none of the given
(iii) (a) 0.3
Step-by-step explanation:
Probability = No. of favourable outcomes / Total no. of outcomes
So, taking the probability of taking a red pen,
Let the number of red pens be x and green pens be y.
0.4 = x / 50
0.4 x 50 = x
20 = x
Therefore, there are 20 red pens
No. of green pens = 50 - (20 + 15) (Red pens + Blue pens)
y = 50 - 35
y = 15
Therefore there are 15 green pens
Substituting the probability formula for (ii) bit,
Probability = 15 / 50 = 0.3
So, for (ii) bit, the correct answer is not in options
(iv) the answer is 0.3
The number of red pens in the box are= 20
Probability of taking a green pen is= 0.3
Probability of taking a blue or green pen is=0.6
Given:
Total number of pens in the box=50
Probability of getting a red pen = 0.4
Number of blue pens in the box= 15
To Find:
The number of red pens in the box, Probability of taking a green pen, probability of taking a blue or green pen
Solution:
(i) Probability of an event is = Favorable outcome/ Total outcomes
P(red)= 0.4
0.4= No. of red pen/ 50
Number of Red pens= 50*0.4= 20
(ii) Number of green pens in the box= 50- Number of red pens- Number of green pens
= 50-20-15= 15
P(green)= 15/50= 0.3
(iii) P( blue or green) = P( blue)+ P( green)= 0.3+0.3=0.6
So,
The number of red pens in the box are= 20
Probability of taking a green pen is= 0.3
Probability of taking a blue or green pen is=0.6
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