# Thread: Probability & Expected Value

1. ## Probability & Expected Value

I have a 4-question worksheet and I think I have them all correct except for one:

1) A sorority sold 65 tickets in a raffle for a $480 TV set. What is the expected value of a single ticket if only one ticket wins? - I'm stumped. The other 4 questions I believe are correct--could someone confirm? 2) A box contains 4 blue cards and 3 red cards. If 2 cards are drawn one at a time, find the probability that both are red with replacement and without replacement. - 9/49 with replacement - 1/7 without replacement 3) Two dice are rolled. What are the odds against rolling a sum of 4 or 11? - 31/5 4) In a NASA rocket firing, the probability of success of the 1st stage=70%, 2nd stage=56%, and 3rd stage=80%. What is the probability for success fir the three stage rocket? - (70/100) x (56/100) x (80/100) = 196/625 Thank You! 2. (1) there are 65 tickets in the raffle for the$480 tv. So the probability of winning is 1/65... so expected value of a ticket is $E(V)=Pr(W)\cdot 480=\frac{1}{65} \cdot 480=\7.38$

(2) Probability without replacement;
$\frac{2}{7}\cdot \frac{1}{6}=\frac{1}{21}$
Probability with replacement;
$\frac{2}{7}\cdot \frac{2}{7}=\frac{4}{49}$

3 and 4 look fine to me..

3. Originally Posted by mdenham2
I have a 4-question worksheet and I think I have them all correct except for one:

1) A sorority sold 65 tickets in a raffle for a \$480 TV set. What is the expected value of a single ticket if only one ticket wins?

- I'm stumped.

The other 4 questions I believe are correct--could someone confirm?

2) A box contains 4 blue cards and 3 red cards. If 2 cards are drawn one at a time, find the probability that both are red with replacement and without replacement.

- 9/49 with replacement correct
- 1/7 without replacement correct

3) Two dice are rolled. What are the odds against rolling a sum of 4 or 11?

- 31/5

4) In a NASA rocket firing, the probability of success of the 1st stage=70%, 2nd stage=56%, and 3rd stage=80%. What is the probability for success fir the three stage rocket?

- (70/100) x (56/100) x (80/100) = 196/625

Thank You!
$\frac{\binom{3}{1}}{7}\frac{\binom{3}{1}}{7}=\frac {9}{49}$

$\frac{\binom{3}{2}}{\binom{7}{2}}=\frac{3}{21}=\fr ac{1}{7}$