Question

mr. wong is about to give one of his students a piece of candy for asking a good question in class. he’s going to choose the piece of candy at random out of a bag he brings to class. the following pieces of candy are in the bag: 15 apple gumballs, 4 grape gumballs, 9 apple suckers, and 3 grape suckers. what is the probability that the piece of candy mr. wong chooses is grape or is a sucker? do not round intermediate computations, and round your answer to the nearest hundredth.

Explanation:

Step1: Calculate total number of candies

First, we sum up all the types of candies. The number of apple gumballs is 15, grape gumballs is 4, apple suckers is 9, and grape suckers is 3. So total candies \( n = 15 + 4 + 9 + 3 \)
\( n = 31 \)

Step2: Calculate number of grape or sucker candies

We use the principle of inclusion - exclusion. The number of grape candies (gumballs + suckers) is \( 4 + 3 = 7 \). The number of sucker candies (apple + grape) is \( 9 + 3 = 12 \). But we have double - counted the grape suckers (3), so the number of candies that are grape or sucker is \( (4 + 3)+(9 + 3)-3=4 + 3+9=16 \) (another way: grape gumballs (4) + apple suckers (9) + grape suckers (3) = 16)

Step3: Calculate the probability

The probability \( P \) that a randomly chosen candy is grape or a sucker is the number of favorable outcomes (grape or sucker) divided by the total number of outcomes (total candies). So \( P=\frac{4 + 9+ 3}{31}=\frac{16}{31}\approx0.52 \) (rounded to the nearest hundredth)

Answer:

\( 0.52 \)