Question

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

Answer 1

anyone????????/

Answer 2

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! :)

Answer 3

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

Answer 4

3 is the number of trials