Martha has the unique talent of being able to guess other people’s

Question

Martha has the unique talent of being able to guess other people’s height and weight. For every three people that Martha meets, she consistently guesses the people’s correct height two times, and for every five people that she meets, she consistently guesses the people’s correct weight three 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?

A. 8/27
B. 2/5
C. 49/81
D. 98/125
E. 125/144

A. 8/27
B. 2/5
C. 49/81
D. 98/125
E. 125/144

tallyho_88 · Accepted Answer

Probability that she guesses the height correctly P(h)=2/3
Probability that she guesses the weight correctlyP(w)=3/5

Probability that she guesses both weight and height correctly(P(h)*P(w))=2/3 * 3/5= 6/15
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 =1-6/15=9/15=3/5

For all three occasions P(A)=3/5 * 3/5 * 3/5=27/125

Probability of the event happening atleast once=1- P(A)=1-27/125=98/125

Ans should be D

ShashankDave · Answer

Bunuel 
This solution uses  Compound Event definition .
I understand that if the probability of a single event is P, then the probability of its complement event is 1-P.
But I didn't know that this can also be used in case of compound events, such as is used here. does the gmatclub math book has this concept discussed? can you please suggest some reading?

sahilvijay · Answer

LETS CONSIDER FOR FIRST PERSON SHE VIEWS=>

XH W , XH XW , H XW IN THESE 3 WAYS SHE CAN SAY WRONG RESULTS FOR SINGLE PERSON
SO P(H) = 2/3 , P(W) = 3/5
XH W = 1/3 x 3/5
XH XW = 1/3 x 2/5
H XW= 2/3 x 2/5

total = 9/15
= 3/5

She can go wrong for single person in probability = 3/5
so for 3 persons she can go wrong in 3/5 x 3/5 x 3/5 = 27/125

Therefore at least 1 correct = 1- Probability none correct 
 = 1-27/125
= 98/125

Hence Option D

hellosanthosh2k2 · Answer

Probability of guessing correct height and weight of a single person =  2/3 * 3/5  = 2/5
Probability of failing to guess correct height and weight of a single person =  1 - (2/5)  = 3/5 (this includes all combo, {H success, W failure}, {H failure, W success}, {H failure, W failure}}

Probability of guessing correct height and weight of 3 persons atleast once = 1 - Probablity of not guessing correct height weight of three persons single time
 = 1 - (Probability of failing to guess correct height and weight of a single person ^ 3)
 =  1 - (3/5)^3  = 98/125

MS26 · Answer

Prob of Correctly Guessing Height P(H)=2/3,
Prob of Correctly guessing wt P(W)=3/5, 
Prob of Correctly Guessing of both P(H&W)=2/5 and like wise Prob of Not-Correctly Guessing of both P(H̅&W̅)=3/5
now question is asking for guessing correctly at least once, in such cases it becomes easier to find 1-(all cases of not guessing correctly) = 1-(3/5*3/5*3/5)=1-(27/125)=98/125(D)

Martha has the unique talent of being able to guess other people’s

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