reading comprehention problem. would love your opinion

ogry

New Member
#1
so, i just had this test. and the solution for it has already been published.
the thing is, i realy dont agree with their explenation for one of the questions so here it is.
10 students are competting in long jump
their jupmps are uniformly distributed between 3 and 5 meters. the jumps are independent for each student.
whats the probability that the two longest jumps were over 4.4 meters.

my solution: chances that one student will jump over 4.4: (5-4.4)/2=0.3
therfore the probability is binomian with n=10 k=2 and p=0.3
so we get the answer is 10!/(2!*8!)*0.3^2*0.7^8=0.233

now acording for their solution we are looking for the probability that "at least" two jump are over 4.4 wich would again give the binomian model with same parameters but we have to sum from k=2 to 10. which would give the answer 0.85.

now what i dont get is, if your asking for the two longest jumps, you nessecerily mean that all the other jumps were under 4.4 and therefor you cant take into account the probabilities that more the 2 students got more then 4.4

just curiouse what you think.
 

JesperHP

TS Contributor
#2
The two longest jumps were over 4.4 meters if
2 are over 4.4 or 3 are over 4.4 or 4 are over 4.4 or 5 are over 4.4 or 6,7,8,9,10 are over 4.4
which offcourse is 1 - the probability that only 0 or 1 is over.

if the jums were 4.5 , 4.5 , 4.5 ,...,4.5, 4.9, 4.10
they are all over 4.4 and the two longest are also over 4.4
hence that the two longest are 4.4 does not imply the other are under 4.4