Binomial Probability Question

[laryxle]

Okay, so I was doing a May 2010 P2 for Maths SL today and had no idea how to work out this question:

7: For game B, the probability that Evan wins is p. He plays game B 7 times.

b) write down an expression, in terms of p, for the probability that he wins exactly four games

That was no problem, I got 35(p)^4(1-p)^3 which is correct

c) Hence, find the values of p such that the probability that he wins exactly four games is 0.15

Okay so I went 0.15=35(p)^4(1-p)^3, but I got lost after this. The answers are p=0.356, 0.770, and in the markscheme out of the 3 possible marks for ©, you get 1 for setting it up like I did and 2 for the answers, so you must be able to do this on your calculator. But how??? Help please Thanks

[genepeer]

this is an equation, 35(p)⁴(1-p)³-0.15=0 The easiest way to solve it is by sketching a graph of that with the windows set 0<x<1 (because probability is between 0-1) and -2<y<2, and then find the zeroes of the equation using the calculator. Haven't tried that 'cause i don't have a calc with me but that's how i'd do it.

Edited October 27, 2010 by Gene-Peer