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 one head and one tail, on either coin?
a. p(1 head and 1 tail) = 2/4 = 1/2
b. p(1 head and 1 tail) = 3/4
c. p(1 head and 1 tail) = 4/4 = 1
d.

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 4 total possible outcomes.

Step2: Count favorable outcomes

The favorable outcomes (one head and one tail) are (penny - head, dime - tail) and (penny - tail, dime - head), which is 2 outcomes.

Step3: Calculate probability

The probability formula is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(1\text{ head and }1\text{ tail})=\frac{2}{4}=\frac{1}{2}$.

Answer:

a. $P(1\text{ head and }1\text{ tail})=\frac{2}{4}=\frac{1}{2}$