Question

A die is loaded in such a way that an even number is twice likely to occur as an odd number. If the die is tossed twice, find the probability distribution of the random variable X representing the perfect squares in the two tosses.

Answer 1

let the probability of odd no be `p`
let the probability of even no be `2p`
`p+p+p+2p+2p+2p =1`
`9p = 1 `
`p = 1/9`
let x= perfect square
x = 4,9
`p(x)= P(x) or p(9) = p(4) + p(9)`
`p(x) = p.p + 2p.2p +p.p + p.2p + 2p.p + p.2p + 2p.p`
`p^2 + 4p^2 + p^2 + 8p^2 = 14p^2`
`p(x) = 14p^2`
`= 14* 1/9^2 = 14/81`