Tickets numbered 2, 3, 4, 5,....., 100, 101 are placed in a box and mi

1.	Tickets numbered 2, 3, 4, 5,....., 100, 101 are placed in a box and mix thoroughly one ticket is drawn at random from the box. Find the probability that the number on the ticket is (i) An even number(ii) A number less than 16(iii) A number which is a perfect square (iv) A prime number less than 40.
Answer» All possible outcomes are 2, 3, 4, 5,......, 101 Number of all possible outcomes = 100 (i) Out of these the numbers that are even = 2, 4, 6, 8,......,100 Let E₁ be the event of getting an even number. Then, number of favorable outcomes = 50 T_n= 100 ⇒ 2 + (n - 1) x 2 = 100, ⇒ n = 50 therefore, P(getting an even number) = \(\frac{50}{100}\) = \(\frac{1}{2}\) (ii) Out of these, number that are less than 16 = 2, 3, 4, 5,.......,15. Let E₂ be the event of getting a number less than 16. Then, number of favorable outcomes = 14 therefore, P(getting a number less than 16) = \(\frac{14}{100}\) = \(\frac{7}{50}\) (iii) Out of these, number that are perfect square = 4, 9, 16, 25, 36, 49, 64, 81 and 100 Let E₃ be the event of getting a number that is a perfect square. Then, number of favorable outcomes = 9 therefore, P(getting a number that is a perfect square) = \(\frac{9}{100}\) (iv) Out of these, prime number less than 40 = 2,3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37. Let E₄ be the event of getting a prime number less than 40. Then, number of favorable outcomes = 12 Therefore, P(getting a prime number less than 40) = \(\frac{12}{100}\) = \(\frac{3}{25}\)

Tickets numbered 2, 3, 4, 5,....., 100, 101 are placed in a box and mix thoroughly one ticket is drawn at random from the box. Find the probability that the number on the ticket is (i) An even number(ii) A number less than 16(iii) A number which is a perfect square (iv) A prime number less than 40.

Answer»

All possible outcomes are 2, 3, 4, 5,......, 101

Number of all possible outcomes = 100

(i) Out of these the numbers that are even = 2, 4, 6, 8,......,100

Let E₁ be the event of getting an even number.

Then, number of favorable outcomes = 50

T_n= 100

⇒ 2 + (n - 1) x 2 = 100,

⇒ n = 50

therefore, P(getting an even number) = \(\frac{50}{100}\) = \(\frac{1}{2}\)

(ii) Out of these, number that are less than 16 = 2, 3, 4, 5,.......,15.

Let E₂ be the event of getting a number less than 16.

Then, number of favorable outcomes = 14

therefore, P(getting a number less than 16) = \(\frac{14}{100}\) = \(\frac{7}{50}\)

(iii) Out of these, number that are perfect square = 4, 9, 16, 25, 36, 49, 64, 81 and 100

Let E₃ be the event of getting a number that is a perfect square.

Then, number of favorable outcomes = 9

therefore, P(getting a number that is a perfect square) = \(\frac{9}{100}\)

(iv) Out of these, prime number less than 40 = 2,3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.

Let E₄ be the event of getting a prime number less than 40.

Then, number of favorable outcomes = 12

Therefore, P(getting a prime number less than 40) = \(\frac{12}{100}\) = \(\frac{3}{25}\)