Odds of 5 out 5 people being left-handed?

Question

At work today, all five of us were left-handed. We thought that was odd and wondered the odds of that happening. Assuming the chances of one person left handed are 10%, I said the probability was 3.125%: Chances of selecting one person out five from a large population being left handed 50%, two 25% three 12.5% etc. Another person said it was much smaller .001%: .1^5. Who, if anyone, is correct?

Answer 1

It would actually be 0.1^5 if it were completely random and assuming that only 10 percent of the population is left handed. Assuming that 50% of people are left handed is not true, it is well documented there are more right handed people than left.

You can't even really say that picking 5 people at your work is completely random either. This is because people who are into any type of visual arts are more likely to be left handed (right brained) than those who are into physics and mathematics. Thus if you are somehow involved in a "right brained" job then it would be less surprising. Now if you were all involved in a predominantly left brained job and you all were left handed that would be really amazing!

Answer 2

It would actually be 0.1^5 if it were completely random and assuming that only 10 percent of the population is left handed. Assuming that 50% of people are left handed is not true, it is well documented there are more right handed people than left.

You can't even really say that picking 5 people at your work is completely random either. This is because people who are into any type of visual arts are more likely to be left handed (right brained) than those who are into physics and mathematics. Thus if you are somehow involved in a "right brained" job then it would be less surprising. Now if you were all involved in a predominantly left brained job and you all were left handed that would be really amazing!

Edit: Hey the girl at the bottom copied my answer!!!

Answer 3

If 10% of the general population are left handed, then then chances of five randomly selected people all being left handed is: (10%)^5 = .00001 (that is: 1 in 100,000).

The chance would be 3.125% only if the general distribution of left & right handed people were 50/50. For example, the chance of 5 randomly selected people all being the same _gender_ is 3.125%

Answer 4

I think that your estimate of 1 in 10 being left handed is low,but assuming that you are correct the way to figure it is by multiplying the collective odds. 1/10 x 1/10 x 1/10 x 1/10 x 1/10..... 1 in 100,000 chances of randomly picking 5 people who are left handed....Are you sure that there is only 1 of 10 people who are like you and your fellow workers?

Answer 5

Using probability, chances of having one left hander in 100 persons is 10%, so the probability is 1/10

So, 5 person is (1/10)^5 = 0.00001 isit?

Answer 6

If the chances of one person in any given population being left handed is 0.1 (10%) then indeed the other person is correct. as it would be 0.1 ^5

can be used for all situations so if you wanted to find probability that 10 people would be left handed in any given population 0.1^10

Answer 7

It's 0.001%. If you assume that the chance of one person being left handed is 10%, then for each additional person you add, you times the result by 10%. Thus it's 0.1 * 0.1 * 0.1 * 0.1 * 0.1 = 0.00001. The result in this case is not additive, 0.1 + 0.1 + 0.1 + 0.1 + 0.1 = 0.5 is correct for choosing 1 out of any 5.

Answer 8

Nope, since the chances of one person being left handed is 10% therefore of five its 0.1*0.1*0.1*0.1*0.1 = 0.00001

that doesnt make sense really! nope that make this a very rare event, But it was u that came up with 10%, so how can we be sure.