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Match the following lists: |
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Answer» a. P(SUCCESS) = 1/2, P(failure)=1/2 Suppose 'n' bombs are to dropped. Let E be the event that the bridge is destroyed. Then, P(E) = 1 - P(0or 1 success) `=1-(((1)/(2))^(n)+""^(n)C_(1)1/2((1)/(2))^(n-1))` `=1-1/10ge(n+1)/(2^(n))or (2^(n))/(10(n+1))ge1` b. The bag contains 2 red 3 white and 5 black balls. Hence `P(S)=1//5,P(F)=4//5,LetE` be the event of getting a red ball. `P(E) =P(S or FSorFFS or ...]ge1/2` The value of n consistent is 4. c. Let there be x red socks and y blue socks and `x gt y.` Then `(""^(x)C_(2)+""^(y)C_(2))/(""^(x+y)C_(2))=1/2` `or (x(x-1)+y(y-1))/((x-y)(x+y-1))=1/2` Multiplying both sides by `2(x+y)(x+y-1)` and EXPANDING, we get `2x^(2)-2x+2y^(2)-2y=x^(2)+2xy+y^(2)-x-y` REARRANGING, we have `x^(2)-2xy+y^(2)=x+y` or `(x-y)^(2) =x+y` or ` |x-y|=x+y` `Now, x+y le17` `x-y lesqrt17` As x- y must be an integer, so `x-y=4` `therefore x+y=16` Adding both together and dividing by 2 yields `x GE 10.` d. Let the number of green socks be `x gt 0.` Let E: be the event that two socks drawn are of the same colour. `P(E)=P(R R or BB or WW or GG)` `=(3)/(""^(6+x)C_(2))+(""^(x)C_(2))/(""^(6+x)C_(2))` `=(6)/((x+6)(x+5))+(x(x-1))/((x+6)(x+5))=1/5` `implies5(x^(x)-x+6)=x^(2)+11x+30` `or 4x^(2)-16x=0` `x=4` |
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