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:

First Sub - Question: Probability of picking an orange

Step 1: Find total number of fruits

To find the probability, we first need the total number of fruits. There are 4 apples, 6 pears, and 8 oranges. So the total number of fruits $n = 4 + 6+8=18$.

Step 2: Calculate probability of picking an orange

The number of oranges $m = 8$. The probability $P(\text{orange})$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(\text{orange})=\frac{8}{18}=\frac{4}{9}$.

Second Sub - Question: Complement of the event

The event of picking an orange has a complement which is the event of not picking an orange, i.e., picking an apple or a pear.

Step 1: Recall the formula for complement probability

The probability of an event $A$ and its complement $\overline{A}$ satisfy $P(A)+P(\overline{A}) = 1$. We know $P(\text{orange})=\frac{4}{9}$.

Step 2: Calculate the complement probability

So $P(\text{complement})=1 - P(\text{orange})=1-\frac{4}{9}=\frac{9 - 4}{9}=\frac{5}{9}$.

Fourth Sub - Question: Which fruit is more likely to be chosen

Answer:

Picking an apple or a pear

Third Sub - Question: Probability of the complement