Question

Consider an experiment of tossing a coin 6 times. Calculate the probability of getting at least 2 tails
(I have the answer, 0.8906, but I don't know how my teacher got it. Can someone work it out??)

Answer 1

Can think of it as the probability of not getting only 1.

Answer 2

P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

P(2) + P(3) + P(4) + P(5) + P(6) = 1 - P(0) - P(1)

is your difficulty in defineing what it means to be "at least"?

Answer 3

What is the probability of getting 1 or 0 ttails hough?

Answer 4

amistre64 reminded me that it's not just the probability of not getting only 1, but rather the probability of not getting 1 or 0, since none is also a possibility.

Answer 5

This is a binomial situation. If you know the binomial formula, that will help a lot.

Answer 6

I don't know it...

Answer 7

If not, you can think of it this way: if the coin is fair and heads or tails has the same probability, P(T) = P(H) = 0.5, then the probability of not getting any tails is (0.5)^6

Answer 8

The probability of getting only one tails is actually the same, but it could occur during any one of the 6 tosses, so you have to multiply (0.5)^6 by 6.

Answer 9

Now, if you add those two probabilities together, P(0) and P(1) then you'll get the combined probability, P(0 or 1) which is the complement of "at least two." So subtract that sum from 1 to get the probability you are looking for.

Answer 10

Thanks!!

Answer 11

For more complicated situations, I would recommend memorizing or having written down nearby, the binomial formula.
q.v. http://stattrek.com/ap-statistics/formulas.aspx