A red and a black die labelled 1 - 6 are thrown simultaneously, find the probability of:
A number less than 5 on the red die but a total of 10 altogether.
I know the answer is 1/36... however i do not understand why there wasnt an inclusion of a restricted sample space. e.g. Pr(Total 10 | <5 on red die) where: Pr (Total 10 And <5 on red) / Pr(>5 on red) = (1/36)/(4/6) = 1/24
Similarly, A pair of fair dice are rolled. Find the probability that both numbers are odd given that the first die shows a number less than 4.
How come this one involves an inclusion of a restricted sample space?
Please explain in simple terms guys, im not too advance in mathematical terminology. Thnks.