Multiple choice

A bag contains apples and oranges, five in all and atleast one of each, all combinations being equally likely. If one fruit is selected at random from the bag, assuming all fruits are distinguishable,the probability that it is an orange is

  1. $\displaystyle \frac{1}{20}$
  2. $\displaystyle \frac{1}{10}$
  3. $\displaystyle \frac{1}{5}$
  4. $\displaystyle \frac{1}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total fruits = 5. Possible combinations (A,O): (1,4), (2,3), (3,2), (4,1). Each combination is equally likely (1/4 chance). For a chosen combination, the probability of picking an orange is O/5. Total probability = sum of (P(comb) * P(orange|comb)) = (1/4)(4/5 + 3/5 + 2/5 + 1/5) = (1/4)(10/5) = 1/2.

AI explanation

Since the bag contains exactly five fruits with at least one apple and one orange, there are four equally likely composition scenarios for the number of oranges: 1, 2, 3, or 4. Under these equally likely combinations, the expected number of oranges in the bag is calculated as (1 + 2 + 3 + 4) divided by 4, which equals 2.5. Because each individual fruit has an equal chance of being selected and all compositions are equally likely, the overall probability of selecting an orange is the expected number of oranges divided by the total number of fruits, giving 2.5 divided by 5, which equals 1/2.

Keep practicing — related questions