An urn contains 5 green and 2 red balls. One ball is drawn at random and its colour is recorded. This selected ball is then replaced in the urn and 3 more balls of the same colour are added to the urn. Next, another ball is drawn from the urn and its colour is recorded.
A) Find a suitable sample space for that random experiment and assign probabilities to sample points.
B) Find the probability distribution table of the random variable X representing the number of red balls among the two selected ones. Draw the bar chart of X.
C) Draw the cumulative distribution function F(x).
Best Answer
The sample space part is straightforward-- they are only drawing two balls, and the only colors are green and red. So the sample space is ${GG, GR, RG, RR}$, with $GR$ denoting green on the first pick, red on the second, etc.
To assign probabilities, \begin{align} P(GG) &= (5/7)*P(G \mbox{ on second pick } | G \mbox{ on first pick})\\ & = (5/7)* (8/10) \end{align} the others are computed similarly.
For (b) just use $P( \mbox{2 green balls}) = P(GG)$, $P(\mbox{1 green ball, 1 red ball}) = P(GR) + P(RG)$, and $P( \mbox{2 red balls}) = P(RR) $ and compute using part (a).
(C) is just drawing a graph of the probabilities from (b).
Voila!