The probability of the number to be prime is :

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If a number is randomly chosen from the numbers 1,2,3,4, …, 25, then the probability of the number to be prime is
(a) \\ \frac { 7 }{ 25 }
(b) \\ \frac { 9 }{ 25 }
(c) \\ \frac { 11 }{ 25 }
(d) \\ \frac { 13 }{ 25 }

Solution:

There are 25 number bearing numbers 1, 2, 3,…,25
Prime numbers are 2, 3, 5, 7, 11, 13, 17 19, 23 = 9
Probability being a prime number = \\ \frac { 9 }{ 25 } (b)

A box contains 90 cards numbered 1 to 90. If one card is drawn from the box at random, then the probability that the number on the card is a perfect square is
(a) \\ \frac { 1 }{ 10 }
(b) \\ \frac { 9 }{ 100 }
(c) \\ \frac { 1 }{ 9 }
(d) \\ \frac { 1 }{ 100 }

Solution:

In a box, there are
90 cards bearing numbers 1 to 90
Perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81 = 9
Probability of being a perfect square = \\ \frac { 9 }{ 90 } = \\ \frac { 1 }{ 10 } (a)

If a (fair) coin is tossed twice, then the probability of getting two heads is
(a) \\ \frac { 1 }{ 4 }
(b) \\ \frac { 1 }{ 2 }
(c) \\ \frac { 3 }{ 4 }
(d) 0

Solution:

A coin is tossed twice
Number of outcomes = 2 x 2 = 4
Probability of getting two heads (HH = 1) = \\ \frac { 1 }{ 4 } (a)

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