Page 42 - DMTH404_STATISTICS

Statistics

Notes
P B P  0.3 0.05
  D/B


Similarly, (ii) B/D    0.429
P
 
P D 0.035
  D/C
P C P  0.1 0.08


P
and (iii) C/D    0.228
P D 0.035
 
Alternative Method :
The above problem can also be attempted by writing various probabilities in the form of
following table :
A B C Total
P A  D  P B  D  P C  D 
D 0.035
 0.012  0.015  0.008


P  A  D  P B  D  P C  D 
D 0.965
 0.588  0.285  0.092
0.600 0.300 0.100 1.000
Total
0.012
P

Thus A/D  etc.
0.035
Example 2: A box contains 4 identical dice out of which three are fair and the fourth is
loaded in such a way that the face marked as 5 appears in 60% of the tosses. A die is selected at
random from the box and tossed. If it shows 5, what is the probability that it was a loaded die?
Solution.
Let A be the event that a fair die is selected and B be the event that the loaded die is selected from
the box.

3 1
P A
Then, we have    and    .
P B
4 4
Further, let D be the event that 5 is obtained on the die, then
1 6

P

P D/A  and D/B 
6 10
3 1 1 6 11
Thus, P(D) = P(A).P(D/A) + P(B).P(D/B)     
4 6 4 10 40
We want to find P(B/D), which is given by
P B  D  1 6 40 6

P B/D     
P D 4 10 11 11
 
Example 3: A bag contains 6 red and 4 white balls. Another bag contains 3 red and 5
white balls. A fair die is tossed for the selection of bag. If the die shows 1 or 2, the first bag is
selected otherwise the second bag is selected. A ball is drawn from the selected bag and is found
to be red. What is the probability that the first bag was selected?

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