- #1
Cyrus
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2.) A student selects his answers on a true/false examinations by tossing a coin (so that any particular answer has a 0.50 probability of being correct). He must answer at least 70% in order to pass. Find the probability of passing when the number of questions is:
(a) 10 (b) 20 (c) 50 (d) 100
EDIT: None of that multiplication rule crap should apply here, D'OH!
I think this too is another case of the binomial probability; hence:
[tex] X \sim Bin(10,0.5) [/tex]
I must evaluate the cases where,
n=10,20,50,100
Ah! The 70% comes into play for the probablity. I want probablity of greater than 70%, or for values of [tex] X \geq .7n [/tex]
Problem a.)
From the table,
[tex] P(X \geq 7) = 1- 0.945 [/tex]
So,
[tex] P(X \geq 7) = [/tex]5.5%
Not good chances!
Part b.)
[tex] P(X \geq 14) = 1- 0.979 [/tex]
[tex] P(X \geq 7) = [/tex]2.1%
Part c.)
[tex] P(X \geq 35) = 1- 0.99870 [/tex]
[tex] P(X \geq 7) = [/tex]0.13%
Part d.)
[tex] P(X \geq 70) = 1- 1[/tex]
I begrudgingly made a quick for loop in MATLAB to calculate Binomial probablity values as high as n=100, with x =70 and p =.5, It spat out 1.000. So,
The probability of getting a 70% and up is 1-1=0. You ant gota chance.
My advice, don't guess on your exams, always cheat.
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