Martha has the unique talent of being able to guess other people’s height and weight. For every four people that Martha meets, she consistently guesses the people’s correct height three times, and for every six people that she meets, she consistently guesses the people’s correct weight four times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once? Select
A) 8/27 B) 7/8 C) 49/81 D) 98/125 E) 125/144
Probability that she guesses the height correctly P(h)=3/4   Probability that she guesses the weight correctlyP(w)=4/6   Probability that she guesses both weight and height correctly(P(h)*P(w))=3/4 * 4/6= 12/24   Now the Q asks about the probability of this happening atleast once.   We calculate it by finding the probability of not being able to guess in any of the three occasions.   Probability of not being able to guess any no. of times =1-12/24=12/24=1/2   For all three occasions P(A)=1/2 * 1/2 * 1/2=1/8   Probability of the event happening atleast once=1- P(A)=1-1/8=7/8   Ans should be 7/8
<result>B</result>
Martha has the unique talent of being able to guess other people’s height and weight. For every four people that Martha meets, she consistently guesses the people’s correct height three times, and for every six people that she meets, she consistently guesses the people’s correct weight four times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?