## anonymous one year ago Jason tossed a fair coin 3 times. What is the probability of getting a head and two tails in any order? 3 over 8 4 over 8 5 over 8 6 over 8

1. anonymous

anyone????????/

2. Ciarán95

To answer this question, let's look at the possible outcomes to our experiment from tossing the coin 3 times (with each toss independent of one another, and an equal chance of getting a head (H) or a tail (T) each time): 1. We could get 3 heads (H H H) appearing 2. We could get 3 tails (T T T) appearing 3. We could get 1 tail and two heads appearing 4. We could get 1 head and 2 tails appearing Looking at option 3, we can consider the 3 different orders in which we could get 1 tail and 2 heads: T H H, or H T H, or H H T Now looking at option 4, we can consider the 3 different orders in which we could get 1 head and 2 tails: H T T, or T H T, or T T H So, we have 8 possible outcomes overall to this experiment, and 3 of them will give us our desired outcome of 1 H and 2 T. So, this should tell us what the probability of achieving this desired outcome is. Hope that helped! :)

3. Michele_Laino

we have to apply the binomial distribution. If we consider the event "head" a success, then the requested probability, is: $\Large p = \left( {\begin{array}{*{20}{c}} 3 \\ 1 \end{array}} \right) \times {\left( {\frac{1}{2}} \right)^1} \times {\left( {\frac{1}{2}} \right)^2} = ...$

4. Michele_Laino

3 is the number of trials