An urn contains 4 white balls and 6 red balls. Balls are drawn from the urn one at a time without replacement. The random variable Xi is 1 if the i-th ball drawn is red, and 0 otherwise.
a) What is the joint probability mass function of X1 and X2?
b) What is the joint probability mass function of X1,X2 and X3?
So where I'm stuck is in identifying if X1 is when red or if X2 is red? I mean logically I would go from X1 to X10 and get the total probability but I don't think I have to go that far for this question. Just not sure how I should start.
If it is the way I think, then my calculation for a would be: $P(x_1 = 1, x_2 = 1) = 6/10 * 5/9$
$P(x_1 = 1, x_2 = 0) = 6/10 * 4/9$
$P(x_1 = 0, x_2 = 1) = 4/10 * 6/9$
$P(x_1 = 0, x_2 = 0) = 4/10 * 3/9$
And b) would follow a similar pattern. But this time X3 would be involved as well.