A bag contains 4 bananas and 3 apples. 3 fruits are taken out randomly. Find…

Step-by-Step Solution

To find the probability that the 3 fruits drawn are either all apples or all bananas, we calculate the probability of each scenario separately and then add them together, as these are mutually exclusive events.

1. Total number of ways to draw 3 fruits:

   • Total fruits = 4 bananas + 3 apples = 7 fruits.

   • Number of ways to choose 3 fruits from 7 = 7C3.

   • 7C3 = (7 * 6 * 5) / (3 * 2 * 1) = 35.

2. Ways to draw 3 apples:

   • Number of ways to choose 3 apples from 3 = 3C3 = 1.

3. Ways to draw 3 bananas:

   • Number of ways to choose 3 bananas from 4 = 4C3 = 4.

4. Calculate the Probability:

   • The favorable outcomes are drawing either all apples or all bananas.

   • Total favorable outcomes = 1 (apples) + 4 (bananas) = 5.

   • Probability = Favorable outcomes / Total outcomes = 5 / 35.

   • Simplified, this is 1 / 7.