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NCERT Class 12- Mathematics: Chapter – 13 Probability Part 10
Question 30:
Two probability distributions of the discrete random variable X and Y are given below.
Prove .
Answer:
Since, we have to prove that,
From Eq. (i) and (ii) ,
Hence proved.
Question 31:
A factory produces bulbs. The probability that any one bulb is defective is and they are packed in boxes of 10. From a single box, find the probability that
(i) None of the bulbs is defective
(ii) Exactly two bulbs are defective
(iii) More than 8 bulbs work properly
Answer:
(i)
(ii)
(iii)
Question 32:
Suppose you have two coins which appear identical in your pocket. You know that one is fair and one is 2-headed. If you take one out, toss it and get a head, what is the probability that it was a fair coin?
Answer:
Let Event that a fair coin is drawn
Event that two headed coin is drawn
Event that tossed coin get a head
Now using Baye՚s theorem
Question 33:
Suppose that of the people with blood group O are left handed and of those with other blood groups are left handed of the people have blood group O. If a left handed person is selected at random, what is the probability that he⟋she will have blood group O?
Answer:
Blood group ‘O’ | Other than blood group ‘O’ | |
I. Number of people II. Percentage of left handed people |
By using Baye՚s theorem,
Question 34:
Two natural numbers are drawn one at a time, without replacement from the set . Find where .
Answer: