Question

You 

will combine two numbers from 0 to 9. One entry will win PHP 6000, out of 100 total entries, if 

you match the last two digits of the final score in a basketball game. Let X be the net gain from 

the purchase of one entry. What is the mean or the expected value of a person who buys a ticket? 

Illustrate by constructing a probability distribution. 

Answer 1

Total number of ways in which we can choose two numbers $= ^{10}C_2 = 45$

One entry will win PHP6000

Probability that will win the entry  $= \dfrac{45}{100} = 0.45$

Probability that does not win $= \dfrac{55}{100} = 0.55$

Probability distribution can be given as,

Expected value of person who buys a ticket $= 0.45 \times 6000 + 0.55 \times 0 = 2700$

Expected value = 2700