Q. 1 a Football Team Plays a Series of 7 Games Which They Can Either Win (W),Lose (L) Or

04.04.2017

STAT101 Section 1 / Name:
Home Work 3 / Id #
Due at the beginning of the class on 11th April 2017
Please solve the problems at provided space. Don’t add any extra paper.

Q. 1 A football team plays a series of 7 games which they can either win (W),lose (L) or tie (T).

(a) How many possible outcomes can the series have (differentiating betweenW L and LW, i.e. order is important).

(b) How many of these have exactly 3 wins, 4 losses and 1 tie?

Q.2 A student has to answer 10 true-false questions.

(a) In how many distinct ways can this be done?

(b) How many of these will have exactly 5 correct answers?

(c) At most 8 correct answers?

(d) Fewer than 4?

Q. 3 Suppose a license plates containing three letters following by two digits with the first digit not zero. How many different license plates can be printed?

Q.4A coin is biased so that obtaining a head is five times as likely as obtaining a tail. The coin is flipped once. What is the probability of a head? Of a tail?

Q. 5 A tennis magazine estimates the probability that Ali will win the men's tournament next month as 0:25, and the probability that Laila will win the women's tournament as 0.15. If these estimates are correct and the probability that both Ali and Laila wil win their tournament next month is 0.08;

(a) FindtheprobabilitythateitherAliorLailawill wintheirtournamentnext month.

(b) Are the events Ali wins and Laila wins mutually exclusive? Why or why not.

Q. 6 Consider the following table:

Student / 1st year / 2nd year / 3rd year / 4th year
Male / 22 / 14 / 10 / 9
Female / 26 / 18 / 14 / 9

If a student is chosen at random

(a) Find the probability of choosing a 1st year student.

(b) Find the probability of choosing a 1st year or a male student.

(c) Find the probability of choosing a student who is a 1st year and male.

Q. 7 A fair coin is tossed five times. What is the probability of obtaining three heads and two tails?

Q. 8 You go to the shop to buy a toothbrush. The toothbrushes there are red, blue, green, purple and white. The probability that you buy a red toothbrush is three times the probability that you buy a green one; the probability that you buy a blue one is twice the probability that you buy a green one; the probabilities of buying green, purple, and white are all equal. You are certain to buy exactly one toothbrush. For each colour, find the probability that you buy a toothbrush of that colour.

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