Q. 295.0( 2 Votes )

There are three c

Answer :

Let P(A) be the probability of choosing a two-headed coin, P(B) be the probability of choosing biased coin that comes up with head 75% of times and P(C) be the probability of biased coin that comes up with tails 40% of the times


There are a total of 3 coins


P(A) = P(B) = P(C) = …(a)


Let H be the event of getting head after the coin toss


We have to find P(A|H) which means the probability of selecting two-headed coin given that we got heads after selecting and tossing the coin


By Baye's theorem



Now we have to find P(H|A), P(H|B) and P(H|C)


P(H|A) means getting heads given that coin A is chosen


Now coin A has both faces as head hence it will always show up heads


Hence P(H|A) = 1 …(b)


P(H|B) means getting heads given that coin B is chosen


Now it is given that coin B shows heads 75% of the times


Hence P(H|B) = 0.75


P(H|B) = 3/4 …(c)


P(H|C) means getting heads given that coin C is chosen


Now it is given that coin C shows tails 40% of the time


As there are only two options heads or tails on a coin hence remaining 60% will be for heads


Hence P(H|C) = 0.6


P(H|C) = …(d)


Substitute values from equation (a), (b), (c) and (d) in (i)







Hence the probability that the coin was chosen is two-headed is .


OR


First 6 positive integers are 1, 2, 3, 4, 5 and 6


As we have to select 2 numbers the number of ways of selecting two numbers is


Using






Hence the total number of ways is 15


Now X can take values 2, 3, 4, 5 and 6 (why not 1? Because there isn’t any number which is smaller than 1 in first positive integers)


Let X = 2


Which means that among the selected pair 2 is greater hence only 1 pair possible (1, 2)



X = 3


Which means that among the selected pair 3 is greater hence pair possible are (1, 3) and (2, 3)



X = 4


Which means that among the selected pair 4 is greater hence pair possible are (1, 4), (2, 4), (3, 4)



X = 5


Which means that among the selected pair 5 is greater hence pair possible are (1, 5), (2, 5), (3, 5) and (4, 5)



X = 6


Which means that among the selected pair 6 is greater hence pair possible are (1, 6), (2, 6), (3, 6), (4, 6) and (5, 6)



Representing it in a table



Mean is given by






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