Answer to Question #346041 in Statistics and Probability for JB Styles

Question

(Distribution Probability)

1. A small-time bingo card costs P100.00 for 5 games. The prize for the first three games is P5,000.00, the fourth is P10,000.00 and the last prize is P20,000.00. If 1,000 bingo cards are going to be sold and you could only win once, what is the expected value of a ticket?
2. You pick a card from a deck. If it is a face card, you will win P500.00. If you get an ace, you will win P1,000. If the card you picked is red you get P100.00. For any other card, you will win nothing. Find the expected value that you can possibly win. 

Answer 1

1.

Probability of the prize P5,000.00:

$p_1=\frac{1}{1000}\cdot\frac{3}{5}=\frac{3}{5000}$

Probability of the prize P10,000.00:

$p_2=\frac{1}{1000}\cdot\frac{1}{5}=\frac{1}{5000}$

Probability of the prize P20,000.00:

$p_3=\frac{1}{1000}\cdot\frac{1}{5}=\frac{1}{5000}$

The expected value of a ticket:

$E(X)=100\cdot0.999+(100-5000)\cdot3/5000+(100-10000)\cdot1/5000$

$+(100-20000)\cdot1/5000=99.9-\frac{44500}{5000}=99.9-8.9=P\ 91$

2.

Let's say I get X as a bonus.

Then X=0, 100, 500, 1000

There are 52 cards.

P(X=500)=12/52

P(X=1000)= 4/52

P(X=100)=26/52-2/52-6/52 = 18/52 [Exclude events that exists in other possibilities]

P(X=0)=1-12/52-4/52-18/52=18/52

So, the expected value that you can possibly win

E= 0*18/52 + 100*18/52 + 500*12/52 + 1000*4/52=157.7