pete and sean decide to raise money for a charity by having a carnival in their backyard. in one of the games that they set up, the probability that a person will win is 0.4. if robyn plays that game nine times, what is the probability that she wins exactly four times?
A)9C5^5 (0.4)^5 (0.4)^5
B)9C4 (0.5)^4 (0.5)^5
C) 9C4 (0.4)^4 (0.6)^5
D)9C5 (0.4)^5 (0.6)^4
and how did you get really confused on probability formula thx

Question

pete and sean decide to raise money for a charity by having a carnival in their backyard. in one of the games that they set up, the probability that a person will win is 0.4. if robyn plays that game nine times, what is the probability that she wins exactly four times?
A)9C5^5 (0.4)^5 (0.4)^5
B)9C4 (0.5)^4 (0.5)^5
C) 9C4 (0.4)^4 (0.6)^5
D)9C5 (0.4)^5 (0.6)^4
and how did you get really confused on probability formula thx

anonymous · Answer

what does 9C5^5 mean?

anonymous · Answer

oh it's suppose to be 9C5 (0.4)^5 (0.4)^4 sorry

anonymous · Answer

the answer anyway is $$(0,4)^4 * (0,6)^5 * \frac{ 9! }{ 4!5! }$$
where (0.4) is the probability to win and (0.6) is 1 - 0.4 equals the probability to lose. Do you need more explanations why this is the answer?

anonymous · Answer

I guess 9C4 means $$\left(\begin{matrix}9 \ 4\end{matrix}\right) = \frac{ 9! }{ 4!5! }$$ then answer C is equivalent to my solution

anonymous · Answer

why do you substract it by 1

anonymous · Answer

well, what does the probability of 1 mean? It means that the case you're looking at is going to happen EVERY time (100% of the tries). Let p be the probability to win, and q be the probability to lose. In this game we assume that anytime you play, you either win or lose. This OR translates into the language of probability as a '+', that means p+q = 1. 

Because when you look at all possible cases and add them , that is equivalent to calculating the probability of one of the possible cases happening - which happens 100% of the time, hence the probability is 1.

In this example, you the probability to win (p) and the probability to lose (q) are all the possible cases, hence p + q = 1 ==> q = 1-p

anonymous · Answer

okay what do the exponents represents

anonymous · Answer

They're kind of the translation of 'AND' into the language of probability. For example, if you tried once to win the game you had a probability of 0.4. If you tried twice, the probability to win twice would be (0.4) * (0.4) = (0.4)^2. The probability to play 9 times and win 9 games would be (0.4)^9

Similarly, if you played 5 times and lost all 5 games the probability for that would be (0.6)^5

Can you see the scheme here?

anonymous · Answer

yeah!  okay that pretty much sums most of my confusion thank you so much!