21. The probability of a successful rocket launching is 0.8. If rockets are aunched until 3 successful

launchings have been made, what is the probability that exactly 6 attempts will be necessary?.

Choose the closest answer. HINT: the k-th success occurs at the n-th trial if and only if there

are exactly (k-1) successes in the previous (n-1) trials and the n-th trial is a success.

(A) 18%

(B) 4%

(C) 23%

(D) 2%

(E) 40%

22. Shuffle a standard deck of 52 cards and take 10 cards WITH REPLACEMENT at random from

this deck. What is the probability of observing 3 cards with a number (Le. 2,3,...,10 in other

words not a letter card A,J,Q,K) ?. Choose the closest.

(A) 1/1000

(B) 5/1000

(C) 5/100

(D) 3/100

(E) 1/100

23. In a box we put a couple of million white balls but only one thousand black balls. We shake

the box and draw (without looking) one hundred balls from the box. Find the probability of

drawing at least one of the blacks. The closest answer is,

(A) 1--1/2000

(B) 1--1/201

(C) 1-1/20

(D) 1-1/2000

(E)

24. Estimate (using R) the probability that the sum of three rolls of a die is less than 10. Choose

the closest answer.

(A) 0.390

(B) 0.314

(C) 0.375

(D) 0.333

(E) 0.308

25. A lake has N (unknown) turtles living there. Capture m- 100, tag them, and release them

back to the lake. After a while recapture a sample of n 50 turtles. If there are r=2 turtles

tagged in the sample, estimate the unknown total number of turtles in the lake by equating z

to its expected value ± an SD or so, under the hypergeometrie model. The estimated N and

its uncertainty a+b is closest to:

(A) 1500 +507

(B) 150+52

(C) 20001208

(D) 2500 1225

(E) 230+10

26. In how many ways can you list the letters of the word STATISTICS?

(A) 3,628,800

(B) 50,400

(C) 302,400

(D) 100, 800

(E) 604,800

27. A psychiatrist checks a person for 6 personality traits and lists the three strongest on a card

in order of strength. In how many different ways can this card be filled out?