Asked Nov 1, 2019

In a true or false assignment of six questions you obliged to get at least four correct to pass. If you guess the answer to the question, what are the probabilities that 

You pass

You get at least 50% of the answer correct

You get no more than two correct 


Expert Answer

Step 1

Consider X be a random variable that follows binomial distribution which indicates the number of correct answers. The probability of success, p is 0.5 and the number of trials, n is 6.

The basic formula to obtain the probability of a binomial distribution is,


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P(Xx) "C,p (1-p)

Step 2

The probability of passing is,


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P(X2 4) P(X 4)+P(X =5)+ P(X6) 'c.(0.5)' (1-0.5)+c,(0.5)' (1-0.5)1 c(0.5) (1-0.5) 0.2344+0.0937+0.0156 =0.3437

Step 3

The probability of getting at least 50%, th...


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P(X23) P(X24)+ P(X = 3) 0.3437+ C,(0.5) (1-0.5)9 0.3437+0.3125 0.6562


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