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 (head - H or tail - T) and a dime (head - H or tail - T), the possible outcomes are (H,H), (H,T), (T,H), (T,T). So there are \(n = 4\) total possible outcomes.

Step2: Count the favorable outcomes

The favorable outcome for getting two heads is (H,H), and the number of favorable outcomes \(m=1\).

Step3: Use the probability formula

The probability formula is \(P=\frac{m}{n}\). Substituting \(m = 1\) and \(n = 4\) into the formula, we get \(P=\frac{1}{4}\).

Answer:

d. \(P(2\ heads)=\frac{1}{4}\)