Question

two sets of 20 papers by slips numbered 1 to 20 are put in the boxes separately.1 slip each is drawn from each box without looking into it.find probability of drawing two perfect squares?what is probability of drawing atleast one prime number?

Answer 1

Number of perfect squares in the range 1 to 20 = 4
(the numbers are 1,4,9 and 16)
For drawing 2 perfect squares, you should draw a perfect square each time.

P(perfect square) = $\frac{4}{20} = \frac{1}{5}$
P(two perfect squares) = $\frac{1}{5} \times \frac{1}{5} = \frac{1}{25}$

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P(drawing atleast one prime number) = 1 - P(drawing 2 non-prime numbers) 
total primes in the range 1 to 20 = 8
(the primes are 2,3,5,7,11,13,17,19)
total non-primes = 20-8 = 12
P(drawing a non-prime number) = $\frac{12}{20} = \frac{3}{5}$
P(drawing 2 non-prime numbers) = $\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}$

P(drawing atleast one prime number) = $1- \frac{9}{25}= \frac{25-9}{25} = \frac{16}{25}$

Answer 2

Sample space = 20

two perfect square { (1,4),(1,9)(1,16) ,(4,9),(4,16),(9,16)} = 6
 p(e) = 6/20
        = 3/10   or   0.3

at least 1 prime no. ( 2,3,5,7,11,13,17,19) = 8
p(e) = 8/20
      = 2/5   or   0.4