Cards are marked with the numbers from 2 to 151 are placed in a box and mixed thoroughly. One card is drawn at random from this box. Find the probability that the number on the card is (i) a prime number less than 75. (ii) an odd number. (iii) a number which is a perfect square
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Given,
Cards are marked with numbers from 2 to 151
To Find,
The probability that the number on the card is a prime number less than 75=?
The probability that the number on the card is an odd number =?
The probability that the number on the card is a number that is a perfect square =?
Solution,
The total numbers in the sample space = 151 - 1 = 150
The prime numbers less than 75 = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73)
Total prime numbers less than 75 = 21
The probability that the number on the card is a prime number less than 75 = 21 /150 = 7 / 50
The number of odd numbers between 2 to 151 = 75
The probability that the number on the card is an odd number = 75 / 150
The probability that the number on the card is an odd number = 1/2
The perfect square number between 2 and 15 = (4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144)
The probability that the number on the card is a number that is a perfect square = 11 / 150
Hence, the probabilities that the number on the card is a prime number less than 75, an odd number, and a number that is a perfect square are 7/50,1/2 and 11/150 respectively.