Question

a. It is determined that one out of every 11 people is left-handed. If 8 people are randomly selected, what is the probability that at most 1 is left-handed?

b. A test given to detect the HIV Aids virus in a person produces a false positive 1 out of every 500 times, which means a person who does not have the virus has test results they say they do. If 50 people are tested, what is the probability that 1 or 2 people tests positive even though they do not have the virus?

c. In an ESP test, a card is marked with one of 4 symbols. A subject, who is blindfolded, is then ask to identify the symbol on the card. If the subject just guesses, and is asked to identify 6 cards, what is the probability of getting 4 correct?

d. A multiple choice test is given, in which each question has 3 possible answers. As part of an experiment in how students approach test-taking, the probabilities for getting answers correct just by guessing are calculated. If the test has 20 questions, what is the probability of getting 4 questions correct?

Answer 1

a)

Sample size , n =    8
Probability of an event of interest, p = 1/11

  
P ( X = 0) = C (8,0) * (1/11)^0 * ( 1 - 1/11)^8=      0.4665
P ( X = 1) = C (8,1) * (1/11)^1 * ( 1 - (1/11))^7=   0.3732
P(at most 1) = P(X≤1) =  0.8397

b)

n=50

p=1/500=0.002

P ( X = 1) = C (50,1) * 0.002^1 * ( 1 - 0.002)^49=      0.0907
P ( X = 2) = C (50,2) * 0.002^2 * ( 1 - 0.002)^48=      0.0045

P(x=1) + P(x=2) = 0.0951

c) P ( X =    4   ) = C(6,4) * 0.25^4 * (1-0.25)^2 =            0.0330   (answer)

d) P ( X =    4   ) = C(20,4) * (1/3)^4 * (1-1/3)^16 =            0.0911   (answer)