Question

A fair decimal die is tossed five times. Find the probability of obtaining an odd number of even digits.

Answer 1

`(3)/(32)`

Explanation:

Well, an even decimal die has probability 0.5 of rolling even and 0.5 of rolling odd.

->The chances of rolling exactly one even number on five rolls is

`P(even).(P(odd))^4= 0.5 * 0.5^4 =>0.5^5=>(1)/(32)`

->The chances of rolling exactly three even numbers on five rolls is

`(P(even))^3.(P(odd))^2= 0.5^5*0.5^2=0.5^5=>(1)/(32)`

The chances of rolling exactly five even numbers on five rolls is
`(P(even))^5=0.5^5=> 1/32`

Further, the probability of independent events is the sum of their probabilities, so the probability of rolling an odd number of even numbers is
`(3)/(32)`