Question

In a forest, there are tigers, hare, and deer. On a given day, the probability of a tiger hunting a hare is 0.35, a deer is 0.25, and either a hare or a deer is 0.55. The probability of a tiger hunting both a hare and a deer on a given day is \_\_\_\_\_\_\_\_, (Round off to two decimal places).

Hint:

For probability questions involving "or" conditions, use the inclusion-exclusion principle: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B). \] Rearrange to find the probability of simultaneous events if needed.

Answer 1

Step 1: Using the principle of inclusion-exclusion. The formula for the union of two events is: \[ P(\text{Hunting a hare or a deer}) = P(\text{Hare}) + P(\text{Deer}) - P(\text{Hare and Deer}). \] Given: \[ P(\text{Hare or Deer}) = 0.55, \quad P(\text{Hare}) = 0.35, \quad P(\text{Deer}) = 0.25. \] Substitute the values into the formula: \[ 0.55 = 0.35 + 0.25 - P(\text{Hare and Deer}). \] Step 2: Solve for \( P(\text{Hare and Deer}) \). Rearrange the equation: \[ P(\text{Hare and Deer}) = 0.35 + 0.25 - 0.55 = 0.05. \]