A bag contain 80 balls numbered 1,...,80. before the game starts, you choose 10 different numbers from among 1,..80 and write them on piece of paper. then 20 balls are selected with out replacement out of the bag at random.

a. What is the probability that all your numbers are selected?

b. What is the probability that none of your numbers is selected?

c. What is the probability that exactly 4 of your numbers are selected?

a. 0.24094

b. 0.2494

c. 0.1473

Step-by-step explanation:

The total probability of choosing any 20 random balls out of 80 is . We use combination since the order of selection does not matter

a. P(all numbers are selected)

are our numbers, is the selection of other ten numbers apart from our numbers.

b. P(none of them are selected)

Since none of our numbers are selected, we assume that all the numbers selected are from the other 70.

c. P (exactly four are selected)

Only four from our numbers are selected and the rest 16 from the other 70 numbers.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.