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varsha jayant karandikar Grade: 12
        Q1) a coin is tossed n times. What is the chance that the head will present itself odd number of time?



A)2^n/n-1
B)2^n/n
C)1/2
D)1/2^n

Q2)There are 4 addressed envelops and 4 letters. Then the probability that all the letters are not mailed through proper envelop is:
A)1/24
B)1
C)23/24
D)3/4
8 years ago

Answers : (3)

Pratham Ashish
17 Points
										

Dear Varsha ,


2nd ques is quite straight forward as


we can send  the letters and envelopes in 4! different ways out of which there will be only one way that letters are mailed properly wid der envelopes then


according to d quest, all letters are not mailed properly which means total ways minus one way of proper mail,


p = (4! - 1)/ 4! = 23/24


ans = (c)


 

8 years ago
Pratham Ashish
17 Points
										

Dear Varsha ,


Q 1


if d coin is tossed n times ,den total possibilities will be 2^n.


let chance of getting r head out of n be nCr


den total way of getting odd times head will be nC1 + nC3+ nC5 +.......nCn (if n is odd) 0r nC1 + nC3+ nC5 +.......nC(n-1) ,for n is even


nw, (1 + x)^n = nC0+ nC1 x + nC2 x^2+........


put x=1 , 2^n = 1 + nC1 + nC2 +......


put x = -1, 0 = 1 - nC1 + nC2 - nC3 +......


just take difference of d above 2 eqn ,


2^n = 2( nC1 + nC3 +........)


if n is odd den


nC1 + nC3+ nC5 +.......nCn = 2^(n-1), probability,p = 2^(n-1)/2^n = 1/2.


 

8 years ago
Pratham Ashish
17 Points
										

hi varsha ,


Q2


toatal no of ways in which 4 letters n  4 envelopes can be arranged is 4!


der can be only 1 way in which in which all letters are mailed properly wid der envelopes.


so required probability,p = (4!-1)/4!   [ all d letters not mailed properly = total ways - no of way in which dey r mailed properly ]


p = 23/24

8 years ago
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