Question

1. cadie is going to toss three coins simultaneously. what is the probability that exactly two of the coins will land on heads?

a. $\frac{1}{6}$
b. $\frac{1}{4}$
c. $\frac{1}{3}$
d. $\frac{3}{8}$

Explanation:

Step1: Calculate total outcomes

Each coin has 2 possible outcomes. For 3 coins, the total number of outcomes is $2\times2\times2 = 2^3=8$ by the multiplication principle.

Step2: Calculate favorable outcomes

Use the combination formula $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 3$ (number of coins) and $k=2$ (number of heads). $C(3,2)=\frac{3!}{2!(3 - 2)!}=\frac{3!}{2!1!}=\frac{3\times2!}{2!×1}=3$.

Step3: Calculate probability

The probability $P$ of an event is the number of favorable outcomes divided by the total number of outcomes. So $P=\frac{3}{8}$.

Answer:

D. $\frac{3}{8}$