Question: Let a die is loaded in such a way that prime number faces are twice as likely to occur as a non prim...

Question

Let a die is loaded in such a way that prime number faces are twice as likely to occur as a non prime number faces. The probability that an odd number will be show up when the die is tossed is

Answer 1

Solution

Given, prime numbers are 2, 3, 5, and non-prime number are 1, 4, 6.

Let weight assigned to non-prime number is ω, then weight assigned to prime number is 2ω.

∴ ω + 2ω + 2ω + ω + 2 ω + ω = 1

or, ω = 1/9

If E be the event of getting on odd face, then

P(5) = ω + 2ω = 5ω = 5/9