Question

You are playing a game of chance that you have a 43% chance of winning. If you play it five times in a row, what is the probability that you will win 3 or more times?

Answer 1

We want probabilty of 3 or more times winning.

That can be broken down:

Win 3 times + Win 4 times + Win 5 times

First,

P(Win) = 0.43

P(Loss) = 1 - 0.43 = 0.57

Now,

P(win 3 or more times) = P(WWWLL) + P(WWWWL) + P(WWWWW)

Where

W is probabilty of winning

L is probability of losing

First,

P(WWWLL) = 0.43 * 0.43 * 0.43 * 0.57 * 0.57 = 0.0258

P(WWWWL) = 0.43 * 0.43 * 0.43 * 0.43 * 0.57 = 0.0195

P(WWWWW) = 0.43 * 0.43 * 0.43 * 0.43 * 0.43 = 0.0147

So,

P(win 3 or more times) = 0.0258 + 0.0195 + 0.0147 = 0.06