Assume that you select two 3-digit numbers at random from the set of consecutive integers from 000 through 999. The selections a
re made with replacement and are independent of one another. If the two numbers are the same, you make $700. If they are different, you lose $2. A random variable XX is defined as your gain or loss. How many different values are possible for the random variable XX
from 000 to 999 makes a total of 1000 numbers from which we are selecting two numbers with replacement. This means that the possible combinations will be double of 1000.
1000 * 1000 = 1000000
to have the same number twice means that the possible combinations will be only 1000. (As there are only 1000 numbers).
But whether they are same or not there will be only two possible values of XX , 2 dollars or 700 dollars which will be the loss or gain for one trial, as the numbers picked will either be same or different.
So if there are 5 choices and only one is correct, there is a 1/5 chance of being correct. since there was 2 questions, you need to multiply 1/5 by 1/5 to get 2/25 of getting both questions correct.
