First make a table of outcomes.
.
Now that is the last row in the table.
Moreover, . Do you see why?
. That happens in the second and third rows.
Whereas . That happens only in the sixth row.
Now you finish off the table.
Three balanced coins are tossed independently. One of the variable of interest is , the number of heads. Let denote the amount of money won on a side bet in the following manner. If the first head occurs on the the first toss, you win $1. If the first head occurs on toss 2 or on toss 3 you win $2 or $3, respectively. if no heads appear, you lose $1.
a) Find the joint probability function for .
b) What is the probability that fewer than three heads occur and you will win $1 or less?
I have no clue on how to do this problem...