Question

at a community event, 150 people were given 1 raffle ticket each. of those raffle tickets, 5 of the tickets will win a gift card, and 3 will win a tv. what is the probability of winning a gift card or tv? p(gift card or tv) = ?% round your answer to the nearest whole percent

Explanation:

Step1: Find total winning tickets

To find the number of tickets that win a gift card or a TV, we add the number of gift card - winning tickets and TV - winning tickets. Let the number of gift card - winning tickets be \(n(G)=5\) and the number of TV - winning tickets be \(n(T) = 3\). Since a ticket can't win both a gift card and a TV (mutually exclusive events), the number of tickets that win either a gift card or a TV is \(n(G\cup T)=n(G)+n(T)\).
\(n(G\cup T)=5 + 3=8\)

Step2: Calculate the probability

The total number of tickets is \(N = 150\). The probability of winning a gift card or a TV is \(P(G\cup T)=\frac{n(G\cup T)}{N}\).
Substitute \(n(G\cup T) = 8\) and \(N=150\) into the formula: \(P(G\cup T)=\frac{8}{150}\)

Step3: Convert to percentage and round

First, calculate \(\frac{8}{150}\approx0.0533\). To convert to a percentage, multiply by 100: \(0.0533\times100 = 5.33\%\). Rounding to the nearest whole percent gives \(5\%\).

Answer:

\(5\%\)