Question

There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that a card drawn shows,

i. a natural number. 

ii. a number less than 1.

iii. a whole number. 

iv. a number greater than 5.

Answer 1

Sample space, 

S = {0, 1, 2, 3, 4, 5} 

∴ n(S) = 6 

i. Let A be the event that the card drawn shows a natural number.

∴ A = {1,2,3,4,5} 

∴ n(A) = 5

∴ P(A) = \(\frac{n(A)}{n(S)}\)

∴ P(A) = 5/6

ii. Let B be the event that the card drawn shows a number less than 1. 

∴ B = {0}

∴ n(B) = 1

∴ P(B) = \(\frac{P(B)}{n(S)}\)

∴ P(B) = 1/6

iii. Let C be the event that the card drawn shows a whole number. 

∴ C = {0,1, 2, 3, 4, 5} 

∴ n(C) = 6

∴ P(C) = \(\frac{n(C)}{n(S)}\) = 6/6

∴ P(C) = 1

iv. Let D be the event that the card drawn shows a number greater than 5. 

Here, the greatest number is 5. 

∴ Event D is an impossible event. 

∴ D = { }

∴ P(D) = \(\frac{n(D)}{n(S)}\)= 0/6

∴ P(D) = 0

∴ P(A) = 5/6; P(B) = 1/6; P(C) = 1; P(D) = 0