SOLUTION: if the probability that an event will happen exactly three times in five trial is equal to the probability that it will happen exactly two times in six trials find the probability

Question 847456: if the probability that an event will happen exactly three times in five trial is equal to the probability that it will happen exactly two times in six trials find the probability that it will happen in one trial.
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
(5 choose 3) * (p)^3 * (1-p)^2 = (6 choose 2) * (p)^2 *(1-p)^4

10*p^3*(1-p)^2 = 15 * p^2 * (1-p)^4
cancel out p's and (1-p)'s
10*p = 15(1-p)^2
10p = 15(1-2p+p^2)
10p = 15 - 30p + 15p^2
15p^2 - 40p +15 = 0
5(3p^2-8p+3) = 0
When applying the quadratic formula we get p = 0.4514, 2.2153.
Since 0<=p<=1, we throw out the 2.21 and we get p = 0.4514.

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