Please help me with this probability question:?
Posted by admin in Uncategorized on 05 13th, 2010 | 2 responses
With a Nevada roulette wheel, there are 18 chances in 38 that the ball with land in the red pocket. The wheel is going to be spun many times. Which of the following is a better choice? or are they the same? why?
a) 38 spins and you win a dollar if the ball lands in a red pocket 20 times or more times.
b)76 spins and you win a dollar if the ball lands in the red pocket 40 or more times.
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they are in fact the same because
20/38=40/76
the problem is one of a binomial probability distribution
where p = 18/38 & q = 20/38
and two values of n given to evaluate probabilities : 38 and 76
WITHOUT ANY CALCULATIONS, IT CAN BE SAID
THAT ALTERNATIVE (a) WILL BE BETTER
this is because probabilities are higher towards the ends (tails)
when n is lower and cluster more tightly towards the mean as n is higher
mathematically, this is judged by
COEFFICIENT OF VARIATION = standard deviation /mean
= sqrt(npq) /n = sqrt(pq/n) for a binomial distribution
so it is evident that variability decreases as n increases
my binomial calculator gives the following probabilities:
(a) 31.26 %
(b) 21.06 %
edit:
——
since n > 30 and both np & nq > 5 for both cases,
u can very well use the normal approximation to the binomial
if u don’t hv a binomial calculator
don’t forget continuity correction !
for (a) u want the tail to the right of 19.5
and for (b) the tail to the right of 39.5
answers agree quite well
(a) 31.21 %
(b) 21.18 %
but as i said at the outset, u dnt really need to calculate