SOLUTION: I am begging a tutor to show me how to do these hard homework problems. The probability of winning is 0.45 every time you play a certain game. Suppose you play the game 10 time

Question 468534: I am begging a tutor to show me how to do these hard homework problems.
The probability of winning is 0.45 every time you play a certain game. Suppose you play the game 10
times.
1. (1 point) Find the probability that you will win exactly 4 times. Round answer to three places after the
decimal point.
I used the formula Pr(x-k)= c(n,k) p^k x q^ (n-k)
so... c(10,4) (.45)^4 x (.55)^(10-4)?
2. (1 point) Find the probability that you will win 2 or more times. Round answer to three places after
the decimal point.
c(10,2) x (.45)^2 x (.55)^(8)?
3. (1 point) Find the expected number of times you will win, and the standard deviation. Round both
answers to three places after the decimal point.
I dont even know how to set this one up...
I think my biggest issue is understanding how to find k
Answer by Tatiana_Stebko(1539) (Show Source): You can put this solution on YOUR website!
1. (1 point) Find the probability that you will win exactly 4 times. Round answer to three places after the decimal point.
I used the formula Pr(x-k)= c(n,k) p^k x q^ (n-k)
so... c(10,4) (.45)^4 x (.55)^(10-4) - CORRECT
2. (1 point) Find the probability that you will win 2 or more times. Round answer to three places after the decimal point.
P(win 2 or more times)=P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)+P(10)
The best way to solve this problem by opposite event
P(win 2 or more times)=1-P(win less then 2)
P(win less then 2)=P(0)+P(1)
THEN
P(win 2 or more times)=1-(P(0)+P(1))
P(win 2 or more times)=1-(c(10,0)(.45)^0*(.55)^(10-0)+c(10,1)(.45)^1*(.55)^(10-1))
3.(1 point) Find the expected number of times you will win, and the standard deviation. Round both answers to three places after the decimal point.
E(X)=np
n=10, p=0.45
E(X)=10*0.45=4.5
the standard deviation

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