Cards marked 1,3,5….49 are placed in a box and mixed thoroughly. One card is drawn from the
box. Find the probability that the number on the card is:
(i) a composite number
(ii) not a perfect square
(iii) multiple of 3 and 5.
Answers
Answer:
(i) P (composite number) = 10/25
(ii) P (not a perfect square) = 1 - P P (perfect square) = 1 - 4/25 = 21/25
(iii) P (multiple of 3 and 5) = 2/25
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Step-by-step explanation:
Given:-
Cards marked 1,3,5….49 are placed in a box and mixed thoroughly. One card is drawn from the box
To find:-
Find the probability that the number on the card is:
(i) a composite number
(ii) not a perfect square
(iii) multiple of 3 and 5.
Solution:-
The numbers are marked on the cards = 1,3,5,...,49
They are 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49
Total number of numbers = 25
Total number of all possible outcomes = 25
Composite numbers = 9,15,21,25,27,33,35,39,45,49
Number of favourable outcomes to Composite number = 10
We know that
Probability of an event P(E)
=Number of favourable outcomes/Total number of all possible outcomes
i) Probability of getting a composite number
= Number of favourable outcomes to Composite number / Total number of all possible outcomes
= 10/25
= 2/5
2)
Numbers which are not perfect numbers =
3,5,7,11,13,15,17,19,21,23,27,29,31,33,35,37,39,41,43,
45,47,
Total number of favourable outcomes to not perfect number = 21
Probability of getting a number not a perfect square
= 21/25
3)
The numbers multiples of 3 = 3,6,9,15,21,27,33,39,45
The numbers multiples of 5 = 5,15,25,35,45
The numbers multiples of 3 and 5 = 15,45
Favourable outcomes to multiples of 3 and 5 = 2
Probability of getting a number is a multiple of 3 and 5
= 2/25
Answer:-
1) Probability of getting a composite number=2/5
2)Probability of getting a number not a perfect square =21/25
3)Probability of getting a number is a multiple of 3 and 5= 2/25
Used formulae:-
- Probability of an event P(E)
=Number of favourable outcomes/ Total number of all possible outcomes