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.

a framing bias

step-by-step explanation:

rodrigo is subject to a framing bias i believe.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c