select the correct answer. john is playing a game of darts. the probability that he throws a dart into the…

select the correct answer. john is playing a game of darts. the probability that he throws a dart into the center of the dart board (the bulls eye) is $\frac{1}{10}$. the probability that he throws the dart into the 10 - point ring is $\frac{3}{10}$. what is the probability that he either hits a bulls eye or scores 10 points? a. $\frac{1}{3}$ b. $\frac{2}{3}$ c. $\frac{3}{5}$ d. $\frac{2}{5}$ e. $\frac{1}{4}$

select the correct answer. john is playing a game of darts. the probability that he throws a dart into the center of the dart board (the bulls eye) is $\frac{1}{10}$. the probability that he throws the dart into the 10 - point ring is $\frac{3}{10}$. what is the probability that he either hits a bulls eye or scores 10 points? a. $\frac{1}{3}$ b. $\frac{2}{3}$ c. $\frac{3}{5}$ d. $\frac{2}{5}$ e. $\frac{1}{4}$

Answer

Explanation:

Step1: Identify probability formula

For mutually - exclusive events (A) and (B), (P(A\cup B)=P(A)+P(B)). Here, hitting the Bull's eye and scoring 10 points are mutually - exclusive. Let (P(A)=\frac{1}{10}) (probability of hitting Bull's eye) and (P(B)=\frac{3}{10}) (probability of scoring 10 points).

Step2: Calculate the combined probability

(P(A\cup B)=\frac{1}{10}+\frac{3}{10}=\frac{1 + 3}{10}=\frac{4}{10}=\frac{2}{5})

Answer:

D. (\frac{2}{5})