Probability & Statistics



Probability & Statistics

Midterm Quiz

Student’s name:

1. A coin loaded to come up heads 2/3 of the time, is thrown until a head appears. What is the probability that the even number of tosses is necessary? a

Hints: What kind of distribution should be used?

2. A committee of 5 is chosen from a group of 8 men and 4 women. What is the probability the group contains a majority of women?

Hint: What are the two possibilities corresponding to this condition?

3. A box contains tags numbered 1,2,…, n. Two tags are chosen without replacement. What is the probability they are consecutive integers?

Hints: (1).How many different pairs can be chosen? (2) How man ”consecutive couples” can be chosen? Try a small number n (e.g., n=5 tags) and then move to a general case (3) Find the probability as a ratio of (2) to (1).

(4) In both cases you can either regard or disregard the order. As soon as the choice is the same for both (1) and (2), it won’t affect the probability.

4. If 20% chips produced by a machine are defective, find the probability that out of 5 chips chosen at random (a) 1 (b) at least 2 chips will be defective.

5. In how many ways can 8 people be seated at a round table if (a) they can seat anywhere (b) three of them, Bob, Michael and Jeff, should not sit together (in other words all the arrangements where B, M and J sitting in any order in three consecutive chairs, must be excluded).

Note: Only relative positions are important.

Grading (The Mathematica part will be graded separately)

Each solved problem adds 3 points to your score.

A+: 15 points.

A: 13-14 (4 solved, the 5-th is on the right track, no major errors);

A -: 12 (4 solved)

B +: 10-11 (3 solved, and some progress with the at least one of the rest)

B : 9

B - : 7-8 (two are solved correctly and at least one is partially solved, without any major errors).

Please write your detailed solutions separately and attach them to this page. Sign your name on the top of this page.

(121- 7) –My mark. Please ignore it.

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