# Probability Problem

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• Jan 6th 2012, 03:52 AM
raed
Probability Problem
Dear Colleagues,

I have the following question and hope to help me to solve it.

You randomly choose two days of a week for your holiday.
What's the probability that you chose Saturday and Sunday?

Best Regards,
Raed.
• Jan 6th 2012, 04:25 AM
Ridley
Re: Probability Problem
$P("\text{Saturday and Sunday}")=\frac{2}{7}\cdot \frac{1}{6}$
• Jan 7th 2012, 01:53 AM
raed
Re: Probability Problem
Quote:

Originally Posted by Ridley
$P("\text{Saturday and Sunday}")=\frac{2}{7}\cdot \frac{1}{6}$

Thank you very much for your reply. But from yesterday up to now I try to understand the answer and I do not.

Regards,
Raed.
• Jan 7th 2012, 04:02 AM
Ridley
Re: Probability Problem
The probability of selecting either Saturday or Sunday as the first pick is (since the two events are disjoint): $1/7 + 1/7 = 2/7$

Once you picked one of them for the first pick, you're left with six days and only one favorable outcome, so the probability of selecting the remaining day is 1/6.
• Jan 7th 2012, 05:06 AM
ILikeSerena
Re: Probability Problem
Here's another way to look at it.

The number of ways to pick 2 (different) days from a week is $\binom 7 2$.
There is only 1 favorable outcome (in which you pick Saturday and Sunday).

$P(\textrm{Saturday and Sunday}) = {\textrm{number of favorable outcomes} \over \textrm{total number of outcomes}} = {1 \over \binom 7 2} = {2 \cdot 1 \over 7 \cdot 6}$.