Probability/Likelihood/Odds of Something Happening.

Question

Here's my question/situation.

Let's say there is a group of 100 people in a room and we are randomly picking one person in the group. Lets also assume that 10% of them are left handed. What's the likelihood or odds of a left handed person being picked 5 times in a row? Also how would you express that in a 1 in X format? That is, the likelihood of 5 left handed people being picked in a row has a 1 in X chance of happening.

Thanks so much for your help!

Answer 1

Since the chosen person doesn't go to the pool, the # of people will reduce each time.

You seem to be new to this field, so easiest way to understand it is

$Pr = \dfrac{10}{100}\cdot\dfrac{9}{99}\cdot\dfrac{8}{98}\cdot\dfrac{7}{97}\cdot\dfrac{6}{96} = \dfrac{1}{298,760}$