True/false examinations by tossing a coin

[Cyrus]

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:

$$X \sim Bin(10,0.5)$$

I must evaluate the cases where,

n=10,20,50,100

Ah! The 70% comes into play for the probability. I want probability of greater than 70%, or for values of $$X \geq .7n$$

Problem a.)

From the table,

$$P(X \geq 7) = 1- 0.945$$

So,

$$P(X \geq 7) =$$5.5%

Not good chances!

Part b.)

$$P(X \geq 14) = 1- 0.979$$

$$P(X \geq 7) =$$2.1%

Part c.)

$$P(X \geq 35) = 1- 0.99870$$

$$P(X \geq 7) =$$0.13%

Part d.)

$$P(X \geq 70) = 1- 1$$

I begrudgingly made a quick for loop in MATLAB to calculate Binomial probability 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.

 

[Tide]

But if you always cheat you will eventually get caught! :)

Here's an auxiliary problem for you. If the probability of getting caught cheating on any given day is 1 in 100, what is the probability that you will be caught cheating over the course of, say, the next 2 years? The next 5 years? The next 10 years?

 

[Cyrus]

NOOO! I seriously have TONS and TONS of stat HW due tomorrow and I am trying to learn as I go because my teacher is terrible I think I am going to get a 3/7 on my HW if I am LUCKY. Are my answers right?

 

[Tide]

I get about 17% for (a) and about 5.8% for (b). I'll give you my other numbers after we figure out why our answers differ.