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Statistics

Notes (a) Binomial probabilities (b) Conditional probability

(c) Bayer’s theorem (d) Clanical probability
4. If B , B , . . . , B , are n events which constitute a partition of , and A is an event of positive
1 2 n
probability, then
P(B )P(A|B )
P(B |A)  n r r
r
 P(B )P(AIB )
j
j
1
for any r, 1  r  n.
(a) Binomial probabilities (b) Conditional probability
(c) Bayer’s theorem (d) Clanical probability
5. There are 1000 people. There 400 females and 600 males then find the probability of males.
(a) 0.4 (b) 0.6
(c) 0.16 (d) 2.01

3.8 Review Questions

1. In a city the weather changes frequently. It is known from past experience that a rainy day
is followed by a sunny day with probability 0.4 and that sa sunny day is followed by a
rainy day with probability 0.7. Assume that the weather on any given day depends only
on the weather of the previous day. Find the probability that
(a) a rainy day is followed by a rainy day

(b) it would rain on Saturday and Sunday when Friday was rainy
(c) the entire period from Monday to Friday is rainy given, that the previous Sunday
was sunny.

2. An urn contains 4 white and 4 black balls. A ball is drawn at random, its colour is noted
and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the
urn and then a ball is drawn at random. What is the probability that the second ball is
black?

3. In a community 2 per cent of the people suffer from cancer. The probability that a doctor
is able to correctly diagnose a person with cancer as suffering from cancer is 0.80. The
doctor wrongly diagnoses a person without cancer as having cancer with probability 0.05.
What is the probability that a randomly selected person diagnosed as having cancer is
really suffering from cancer?
4. An explosion in a factory manufacturing explosives can occur because of (i) leakage of
electricity, (ii) defects in machinery, (iii) carelessness of worker or (iv) sabotage. The
probability that
(a) there is a leakage of electricity is 0.20
(b) the machinery is defective is 0.30

(c) the workers are careless is 0.40
(d) there is sabotage is 0.10

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