SOLUTION: if a coin is biased so that P(H)=0.45 and P(T)=0.55 what will be the probability of two heads if a coin is tossed three times

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Question 1039832: if a coin is biased so that P(H)=0.45 and P(T)=0.55 what will be the probability of two heads if a coin is tossed three times
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This is a binomial distribution problem. The formula we will use is

(n C x)*(p^x)*(1-p)^(n-x)

where
p = 0.45 is the probability of heads
1-p = 0.55 is the probability of tails
n = 3 is the number of tosses
x = 2 is the number of heads we want
n C x refers to the combination formula

n C x = (n!)/(x!*(n-x)!)
3 C 2 = (3!)/(2!*(3-1)!)
3 C 2 = (3!)/(2!*1!)
3 C 2 = (3*2*1)/(2*1*1)
3 C 2 = 6/2
3 C 2 = 3

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So let's plug in the given values to get...


(n C x)*(p^x)*(1-p)^(n-x)
(3 C 2)*(0.45^2)*(1-0.45)^(3-2)
(3 C 2)*(0.45^2)*(0.55)^(1)
(3)*(0.45^2)*(0.55)^(1)
(3)*(0.45^2)*(0.55)
(3)*(0.2025)*(0.55)
0.334125

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The final answer is 0.334125