Test Index

NIMCET 2025 Paper

Section: Mathematics

Question : 6 of 120

Marks: +1, -0

0.99

0.01

Solution:

Concept:

The total probability of getting a head is found by considering each coin's contribution, weighted by the chance that coin is chosen.

Formula:

P(\text{Head}) = P(\text{Head} \mid \text{Blue}) \cdot P(\text{Blue}) + P(\text{Head} \mid \text{Red}) \cdot P(\text{Red})

Solution:

Step 1: Probability of choosing each coin is equal:

P(\text{Blue}) = \frac{1}{2}

and

P(\text{Red}) = \frac{1}{2}

Step 2: Given conditional probabilities:

P(\text{Head} \mid \text{Blue}) = 0.99

and

P(\text{Head} \mid \text{Red}) = 0.01

Step 3: Apply the law of total probability:

P(\text{Head}) = (0.99 \times \frac{1}{2}) + (0.01 \times \frac{1}{2})

P(\text{Head}) = \frac{0.99 + 0.01}{2} = \frac{1.00}{2} = 0.5

Answer:

0.5 (Option D)

Go to Question:

Prev Question

Next Question