A bag contains 100 identical tokens, on which numbers 1 to 100 are marked. A token is drawn at random. What is the probability that the number on the token is:(a) an even number (b) an odd number (c) a multiple of 3 (d) a multiple of 5 (e) a multiple of 3 and 5 (g) a multiple of 3 or 5 (h) a number less than 20 (i) a number greater than 70 (j) a perfect square number (k) a prime number less than 20..
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Answer:
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It is given that , we have a bag of 100 marked tokens .
Now we have to find ,
(a) Probability for an even number
Now, from 1 to 100 , even numbers are 2,4,6,8,10,12,..............,100
Hence, there are 50 even number present in between 1 to 100
Hence , probability of even numbered tokens = 50 / 100 = 1/2 = 0.5
(b) Probability for odd number
Now , from 1 to 100 , odd numbers are 1,3,5,7,9,11,.............,99
Hence, there are 50 odd numbers in between 1 and 100
Hence , probability of odd numbered tokens = 50 / 100 = 1/2 = 0.5
(c) Probability of a number which is a multiple of 3
Now , from 1 to 100 , multiples of 3 are : 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99
Hence, there are 33 multiples of 3 in between 1 and 100
Hence probability of multiples of 3 = 33 / 100 = 0.33
(d) Probability of number which is multiples of 5
Now , from 1 to 100 multiples of 5 are :
5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100
Hence , there are 20 multiples of 5 in between 1 and 100
Hence , probability of multiples of 5 = 20 / 100 = 1 / 5 = 0.2
(e) Probability of number which is the multiples of 3 and 5
Now , from 1 to 100 multiples of 3 and 5 are : 15,30,45,60.75,90
Hence , there are 6 multiples of 3 and 5
Hence , probability of multiples of 3 and 5 = 6 / 100 = 3 / 50 = 0.06
(f) Probability of number which is the multiple of 3 or 5
Now , from (c) and (d) , total number of multiples of 3 and 5 are 53
Hence , probability of multiples of 3 or 5 = 53 / 100 = 0.53
(g) Probability of number less than 20
There are 19 numbers which are less than 20
Hence , probability of number less than 20 = 19 / 100 = 0.19
(h) Probability of a number greater than 70
Now , there are 30 numbers which are greater than 70
Hence , probability of number greater than 70 = 70 / 100 = 0.7
(i) Probability of a perfect square
Now , perfect squares between 1 and 100 are : 1,4,9,16,25,36,49,64,81,100
Hence , probability of finding a perfect square = 10 / 100 = 0.1
(j) Probability of finding a prime number less than 20
Now , prime numbers less than 20 are : 2,3,5,7,11,13,17,19
Hence , probability of finding prime numbers less than 20 = 8 / 100 = 0.8