Question

The numbers on a die are replaced by the first six even numbers. The die is rolled once. Find the probability that the number appearing on the die is:

1. greater than 4 
2. divisible by 3 
3. not a multiple of 10

Answer 1

Given: The first six even positive integers are marked on the faces: ({2, 4, 6, 8, 10, 12}).

Total elementary outcomes, \[ n(S) = 6 \]

(i) Greater than 4: Favourable numbers: ({6, 8, 10, 12})

(4 numbers) 

\[ P(\text{number} > 4) = \dfrac{4}{6} = \dfrac{2}{3} \]

(ii) Divisible by 3: Favourable numbers: ({6, 12}) 

(2 numbers) 

\[ P(\text{divisible by } 3) = \dfrac{2}{6} = \dfrac{1}{3} \]

(iii) Not a multiple of 10: Multiples of 10 in the set: ({10}) (1 number)

Numbers that are not multiples of 10: ({2, 4, 6, 8, 12})

(5 numbers) 

\[ P(\text{not a multiple of } 10) = \dfrac{5}{6} \]