Solve by using the quadratic formula. 9p^2 +3 = 16p
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If you flip a coin one time, the probability to get a Head is
p = 1/2
The probability of not getting a head in a single toss is :
q = 1 - 1/2 = 1/2
Thus there is only one unique situation to get the same number of heads and tails : in 10 toss you need to get exactly five heads, it will means that the rest is the tails.
Now using Binomial theorem of probability, the probability of getting exactly x = 5 heads in a total of n = 10 tosses is :
P(X = 5) = ≈ 0.246
So the probability of that is 24,6 %
Good Luck