Question

suppose you flip a penny and a dime. use the following table to display all possible outcomes.

penny	dime
head	?
head	?
tail	?
tail	?

if each single outcome is equally likely, you can use the table to help calculate probabilities. what is the probability of getting two heads?
a. $p(2\text{ heads})=\frac{1}{2}$
b. $p(2\text{ heads})=\frac{3}{4}$
c. $p(2\text{ heads})=\frac{4}{4}$
d. $p(2\text{ heads})=\frac{1}{4}$

Explanation:

Step1: List all possible outcomes

When flipping a penny and a dime, the possible outcomes are (penny - head, dime - head), (penny - head, dime - tail), (penny - tail, dime - head), (penny - tail, dime - tail). So there are a total of 4 possible outcomes.

Step2: Identify the favorable outcome

The favorable outcome for getting two heads is only 1 case: (penny - head, dime - head).

Step3: Calculate the probability

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the number of favorable outcomes for getting two heads is 1 and the total number of outcomes is 4. So $P(2\text{ heads})=\frac{1}{4}$.

Answer:

D. $P(2\text{ heads})=\frac{1}{4}$