# probability question

• February 17th 2010, 06:23 AM
littleprince327
probability question
A dating service finds that 35% of the couples that it matches eventually get married. In the next 150 matches that the service makes, find the probability that at least 20 couples get married.

this is the first time i come across this kind of question...i dun know thw way to handle it.....can anyone possibly help??

• February 17th 2010, 05:42 PM
Danneedshelp
Quote:

Originally Posted by littleprince327
A dating service finds that 35% of the couples that it matches eventually get married. In the next 150 matches that the service makes, find the probability that at least 20 couples get married.

this is the first time i come across this kind of question...i dun know thw way to handle it.....can anyone possibly help??

This sounds like a binomial problem.

Let $X$ denote the number of matched couples that eventually get married. Consequently, the random variable $X$ has a binomial distribution based on $n=150$ trials with success probability $p=0.35$. It follows that,

$P(X\geq\\20)=\sum_{x=20}^{150}\left( \begin{array}{ccc}\\
150\\
x\end{array} \right)\\(.35)^{x}(1-.35)^{150-x}$
.
• February 17th 2010, 11:03 PM
littleprince327
but how can i calculate the answers by calculator??
the formula is so long...
is there any other way which can solve the question simply?
• February 18th 2010, 03:20 PM
Danneedshelp
Quote:

Originally Posted by littleprince327
but how can i calculate the answers by calculator??
the formula is so long...
is there any other way which can solve the question simply?

Binomial Calculator

Binomial Distribution: Probability Calculator

there are all kinds of calculators out there
• February 18th 2010, 05:56 PM
matheagle
Your instructor most likely wants you to use the normal approximation to the binomial distribution.
That's a central limit theorem that was proved by Gauss.