Question

using a tree diagram to find the probability of a compound event
1st coin 2nd coin 3rd coin outcomes
what is the probability of getting 2 heads up and 1 tails up when flipping three coins?
○ $\frac{1}{6}$
○ $\frac{1}{4}$
○ $\frac{3}{8}$
○ $\frac{2}{3}$

Explanation:

Step1: Count total outcomes

There are 8 total outcomes from the tree - diagram: (H,H,H), (H,H,T), (H,T,H), (H,T,T), (T,H,H), (T,H,T), (T,T,H), (T,T,T).

Step2: Count favorable outcomes

The favorable outcomes (2 heads and 1 tail) are (H,H,T), (H,T,H), (T,H,H), so there are 3 favorable outcomes.

Step3: Calculate probability

The probability $P$ of an event is given by $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P = \frac{3}{8}$.

Answer:

$\frac{3}{8}$