1.

A certain coin is tossed with probability of showing head being 'p'. Let 'q' denotes the probability that when the coin is tossed four times the number of heads obtained is even. Then

Answer»

there is no value of `p`, if `q=(1)/(4)`
there is exactly ONE value of `p`, if `q=(3)/(4)`
there are exactly three value of `p`, if `q=(3)/(5)`
there are exactly four value of `p`, if `q=(4)/(5)`

Solution :`(a,c)` We have `q=P(0H or 2H or 4H)`
`:.q=p^(4)+^(4)C_(2)p^(2)(1-p)^(2)+(1-p)^(4)`
`=8p^(4)-16p^(3)+12p^(2)-4p+1`
`=((2p-1)^(4)+1)/(2)`
Now put the values and check.


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