in a kitchen, there are 54 utensils consisting of bowl, plates and glasses. the ratio of bowl , plate glasses is 3:2:1. a utensil is picked at random.find the probability that:- 1. it is a plate. 2. it is not a bowl.
Answers
let the ratio be x
x+2x+3x=54
6x=54
x=54/6
x=9
2x=18
3x=27
1) no.of plate = 18
so probability = 18/54
=1/3
2)when it is not a bowl it's going to be plates and glasses.
no. of plates and glasses together=
27
probability=27/54=1/2
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Given:
Total utensils=54
The ratio of bowls, plates, and glasses=3:2:1
To find:
The probability that a utensil picked at random is
i. a plate
ii. not a bowl
Solution:
The probability that a utensil picked at random is a plate is 1/3 and not a bowl is 1/2.
We can find the probability by following the given steps-
We know that the probability of an event is obtained by dividing the favourable outcomes by the total possible outcomes of that event.
The total number of utensils=54
The ratio of bowls, plates, and glasses=3:2:1
The number of bowls=3/6 of 54
=1/2×54
=27
The number of plates=2/6 of 54
=1/3×54
=18
The number of glasses=1/6 of 56
=1/6×54
=9
i. Now the probability of picking a plate at random=Total number of plates/ Total number of utensils
On putting the values, we get
=18/54
=1/3
ii. Similarly, the probability of not picking a bowl=Total number of utensils that are not a bowl/Total number of utensils
=Total number of plates and glasses/ Total number of utensils
=(18+9)/54
=27/54
=1/2
Therefore, the probability that a utensil picked at random is a plate is 1/3 and not a bowl is 1/2.