Page 33 - DMTH404_STATISTICS

Unit 2: Methods of Enumeration of Probability

4. If each card on an orindary deck of 52 playing cards has the same probability a being Notes
drawn, then find a red king or a black ace?
(a) 1/13 (b) 2/13
(c) 4/52 (d) 4/43

5. If P(A) and P(B) is given then P(A  B) is equal to
(a) P(A) + P(B) + P(AB) (b) P(A) + P(B) – P(AB)
(c) P(A) – P(B) + P(AB) (d) P(A) – P(B) – P(AB)

2.6 Review Questions

1. Prove the following : Space
(a) If P(A) = P(B) = 1; then P(A  B) = P(A  B) = 1.
(b) If P(A) = P(B) = P(C) = 0, then P(A  BC) = 0.
(c) We have mentioned that by convention we take P() = 0.

But see if you can prove it by using P4.
2. Fill in the blanks in the following table :

P(A) P(B) P(A  B) P(A  B)
0.4 0.8 0.3
0.5 0.6 0.25

3. Explain why each one of the following statements is incorrect.
(a) The probability that a student will pass an examination is 0.65 and that he would fail
is 0.45.

(b) The probability that team A would win a match is 0.75, that the game will end in , a
draw is 0.15 and that team A will not loose the game is 0.95.
(c) The following is the table of probabilities for printing mistakes in a book.

No. of printing mistakes 0 1 2 3 4 5 or more
Probability 0.12 0.25 0.36 0.14 0.09 0.07
(d) The probabilities that a bank will get 0, 1, 2, or more than 2 bad cheques on a given
day are 0.08, 0.21, 0.29 and 0.40, respectively.
4. There are two assistants Seema (S) and Wilson (W) in an office. The probability that Seema
will be absent on any given day is 0.05 and that Wilson will be absent on any given day
is 0.10. The probability that both will be absent on the same day is 0.02. Find the probability
that on a given day,
(a) both Seema and Wilson would be present,
(b) at least one of them would be present, and
(c) only one of them will be absent.

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