a box contains 1-100 numbers .find the probability of 1.square numbers 2.prime numbers 3.two digit numbers
Answers
Total outcomes = 100 -1 +1 = 100
( if number is m to n, and n>m, then total numbers there are n - m + 1)
1. No. of squares b/w 1-100 = 10 ( 1, 4, 9, 16, 25, 36, 49, 64, 81, 100)
Thus,
P ( getting square number)
No. of favourable outcomes
= ------------------------------------------
Total no. of outcomes
10
= ------- = 10
100
2. No. of prime numbers = 25 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)
Thus,
P ( getting prime number)
No. of favourable outcomes
= ------------------------------------------
Total no. of outcomes
25 1
= ----------- = ----
100 4
3. 2-digits number = 10 to 100
= 100-10+1
= 91
Thus,
P ( getting 2-digit number)
No. of favourable outcomes
= ------------------------------------------
Total no. of outcomes
91
= ----------- = 0.91
100