Question

A class of 40 students showed that 20% were taller, 40% were shorter and 40% were shortest. Then the probability that the students are either taller or shortest is?

• A. \(0.60\)
• B. \(0.40\)
• C. \(0.20\)
• D. \(0.80\)

Hint:

For mutually exclusive events \(A\) and \(B\), \[ P(A\cup B)=P(A)+P(B) \] because both events cannot occur simultaneously.

Answer 1

The Correct Option is A

Concept: Probability of an event is given by: \[ P(E)=\frac{\text{Number of favourable outcomes}} {\text{Total number of outcomes}} \] When two mutually exclusive categories are involved, the probability of either event occurring is obtained by adding their individual probabilities.

Step 1: Identify the given percentages.
Out of all students: \[ 20\% \text{ are taller} \] \[ 40\% \text{ are shorter} \] \[ 40\% \text{ are shortest} \] The total percentage is: \[ 20+40+40=100\% \] which accounts for all students in the class.

Step 2: Find the probability of selecting a taller student.
\[ P(\text{Taller}) = \frac{20}{100} = 0.20 \]

Step 3: Find the probability of selecting a shortest student.
\[ P(\text{Shortest}) = \frac{40}{100} = 0.40 \]

Step 4: Calculate the probability of either taller or shortest.
Since a student cannot be both taller and shortest at the same time, the events are mutually exclusive. Therefore, \[ P(\text{Taller or Shortest}) = P(\text{Taller}) + P(\text{Shortest}) \] \[ = 0.20+0.40 \] \[ = 0.60 \]

Step 5: Write the final answer.
Hence, \[ \boxed{P(\text{Taller or Shortest})=0.60} \] Therefore, \[ \boxed{\text{Option (A)}} \] is the correct answer.