A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
a) 3/40,000
b) 3/20,000
c) 1/32
d) 1/20,000
e) None of these
Please post the explanations if you know.
E
b
2*(60c1)/1000*800
Ans – A
Probability of picking sibling from first class – 60/1000
Probability of picking sibling to the already selected student – 1/800
So probability of picking 1 pair of siblings is
60/1000 * 1/800 = 3/40 000
a. Take GMAT team, please provide the answer
a: 3/40000
a
for the first time u pick a student in a class of 1000……u have 60 choices……so u have a probablity of 60/1000………and then when u pick a student from the class of 800…..for it to be a sibling pair…..u have jst one option……so u multiply 60/1000 by 1/800…….and hence the answer is A
Go with Talgat’s explanation.
A
Ans A.. Here is another explanation.
Total possible pairs = 800*1000=800000
Total sibling pairs = 60
So prob = 60/800000 = 3/40000
A
A all the way
a
Ans: 3/20000
there are two ways that the selection can take place:
A.
1. select a sibling from the senior group, in this case the probability will be (no.of winners / total) = 60/1000
2. select the pair from the junior group = 1/800 (since the winners is just one)
So probability of event 1 is 60/1000 * 1/800
B.
Else in can occur the other way round..
1. Select a sibling from the junior class and then go on to the senior class.. in this case the probability is 60/800 * 1/1000
Thus total probability is : P(A) + P(B) = [60/1000 * 1/800 ] + [60/800 * 1/800]
= 3/20000
3/20000 ….
@LEES
TOTAL PROBABILITY = P(A) + P(B) IS EITHER EVENT A OR EVENT B OCCURS….BUT IN THIS CASE ITS BOTH EVENT A AND EVENT B HAS TO OCCUR FOR A SIBLING TO BE CHOSEN. HENCE , TOT PROB. = P(A)*P(B)
AND REMEMBER…THE TWO EVENTS OF CHOSING SOMEONE FROM THE JUNIOR CLASS AND SOMEONE FROM THE SENIOR CLASS ARE MUTUALLY INDEPENDENT. SO P = P(A)*P(B)…BECAUSE BOTH EVENTS A AND B HAVE TO HAPPEN FOR A SIBLING TO BE SELECTED.
IF THE QUESTION WAS “WHAT IS THE PROBABILITY THAT A SIBLING IS SELECTED” AND NOT A “SIBLING PAIR” …THEN IT WUD BE TOTAL PROB = P(A) + P(B).