Question

your teacher is giving out fruit for lunch. a paper bag contains 4 apples, 6 pears, and 8 oranges.
what is the probability you will pick an orange at random?
what is the complement to this event?
what is the probability of the complement?
which fruit is more likely to be chosen?

Explanation:

Step1: Calculate total number of fruits

Total fruits = \(4 + 6+8=18\)

Step2: Calculate probability of picking an orange

Probability \(P=\frac{\text{Number of oranges}}{\text{Total number of fruits}}=\frac{8}{18}=\frac{4}{9}\)

Step3: Calculate complement event probability

Complement event (not picking an orange) probability \(=1 - \frac{4}{9}=\frac{5}{9}\)

Step4: Compare probabilities of fruits

Probability of apple \(=\frac{4}{18}=\frac{2}{9}\), probability of pear \(=\frac{6}{18}=\frac{1}{3}\), probability of orange \(=\frac{4}{9}\). Since \(\frac{4}{9}>\frac{1}{3}>\frac{2}{9}\), orange is more likely.

Answer:

1. Probability of picking an orange: \(\frac{4}{9}\)
2. Complement event probability: \(\frac{5}{9}\)
3. Orange is more likely to be chosen.