Question 1192893
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The probability of heads is p; the probability of tails is (1-p).<br>
The probability of getting 2 heads on 7 flips is {{{C(7,2)((p)^2)((p-1)^5)}}}.<br>
The probability of getting 3 heads on 7 flips is {{{C(7,3)((p)^3)((p-1)^4)}}}.<br>
The probabilities of 2 or 3 heads are the same:<br>
{{{C(7,2)((p)^2)((1-p)^5)=C(7,3)((p)^3)((1-p)^4)}}}<br>
{{{21((p)^2)((1-p)^5)=35((p)^3)((1-p)^4)}}}<br>
{{{21(1-p)=35(p)}}}
{{{21-21p=35p}}}
{{{21=56p}}}
{{{p=21/56 = 3/8}}}<br>
ANSWER: p=3/8<br>