Question

a game - show spinner has these probabilities of stopping on particular dollar values: 60% for $50, 25% for $100, 10% for $500, and 5% for $1000. what is the probability of a player winning $500 or $1000?

Explanation:

Step1: Identify relevant probabilities

We need to find the probability of winning $\$500$ or $\$1000$. The probability of winning $\$500$ is $10\%$ and the probability of winning $\$1000$ is $5\%$.

Step2: Use the addition rule for mutually - exclusive events

Since winning $\$500$ and winning $\$1000$ are mutually - exclusive events (a spinner can't land on two different amounts at the same time), we use the formula $P(A\cup B)=P(A)+P(B)$. Let $A$ be the event of winning $\$500$ and $B$ be the event of winning $\$1000$. Then $P(A) = 0.1$ and $P(B)=0.05$.

$$P(A\cup B)=0.1 + 0.05$$

Answer:

$15\%$