Unfair Coin!

Probability Level 2

I have an unfair coin. When I toss the coin, it gives more heads than tails.

I am going to throw this unfair coin twice. The chances that I will get 1 heads and 1 tails is:

Higher than 50% 50% Lower than 50%

Winston Choo by Winston Choo , 46, Singapore

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1 solution

Parth Sankhe
Dec 13, 2018

1 head and 1 tails would have a probability of 2 p ( 1 − p ) 2p(1-p) .

= 4 p − 4 p 2 2 \frac {4p-4p^2}{2}

= 1 2 − 4 p 2 − 4 p + 1 2 = 1 2 − ( 2 p − 1 ) 2 2 ≤ 1 2 =\frac {1}{2} - \frac {4p^2-4p+1}{2}=\frac {1}{2} - \frac {(2p-1)^2}{2} ≤ \frac {1}{2}

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