Question

There are two coins, say blue and red. For the blue coin, the probability of getting heads is 0.99 and for the red coin, it is 0.01. One coin is chosen randomly and is tossed. The probability of getting heads is:

• A. 1
• B. 0.98
• C. 0.5
• D. 0.02

Hint:

When choosing between multiple options with different probabilities, use the law of total probability to account for all possible outcomes.

Answer 1

The Correct Option is C

We are given that there are two coins: the blue coin with a probability of getting heads \( P(\text{Heads|Blue}) = 0.99 \) and the red coin with \( P(\text{Heads|Red}) = 0.01 \). One of these coins is chosen randomly. The probability of getting heads is calculated as follows:

Step 1: Use the law of total probability.
The total probability of getting heads is: \[ P(\text{Heads}) = P(\text{Heads|Blue}) \cdot P(\text{Blue}) + P(\text{Heads|Red}) \cdot P(\text{Red}) \] Since the coin is chosen randomly, the probability of choosing each coin is \( \frac{1}{2} \). Thus: \[ P(\text{Heads}) = 0.99 \cdot \frac{1}{2} + 0.01 \cdot \frac{1}{2} = \frac{0.99 + 0.01}{2} = \frac{1}{2} = 0.5 \] Thus, the correct answer is \( 0.5 \), corresponding to option (c).