0
$\begingroup$

The probability of getting a Powerball ticket with no matching white balls and a matching powerball is $0.0263$. The probability of getting a powerball ticket with a matching white ball and a matching powerball is $0.01087$. Each of those tickets have a winning prize of $\$4$. The probability of winning any prize is $0.0404$.

If you win a prize, what is the probability that it is a $4$ dollar prize?

I think this is a conditional probability problem with $T_4$ being the event that you win any 4 dollar prize (this would have a probability of 0.03717, being the sum of both of the aforementioned tickets) and $W$ being the event that you win. I THINK the problem should be set up as $P(T_4|W)$.

I ended up getting this to $P(T_4 \cap W)/P(W)$ but I don't know how to proceed forward. I would convert $P(T_4\cap W)$ to $P(T_4)P(W)$ but I don't know for a fact that they're independent.

Advice?

  • 4
    No. $T_4$ and $W$ are not independent—in fact, $T_4 \subset W$, so $P(T_4 \cap W) = P(T_4)$. – 2017-01-27
  • 0
    That was what I needed to know. Thanks – 2017-01-27
  • 0
    Indeed. That is to say: If you win a $\$4$ prize, then you have won a prize. How can they be independent? – 2017-01-27

0 Answers 0