Question

A coin is biased so that the probability of obtaining a head is 0.25. Another coin is biased so that the probability of obtaining a tail is 0.4. If both the coins are tossed together, the probability of obtaining at least one head is:

• A. \( \frac{3}{10} \)
• B. \( \frac{1}{5} \)
• C. \( \frac{7}{10} \)
• D. \( \frac{4}{5} \)

Hint:

To solve probability problems involving at least one occurrence of an event, use the complement rule: \( P(\text{at least one head}) = 1 - P(\text{no heads}) \).

Answer 1

The Correct Option is C

The probability of obtaining at least one head is the complement of the probability of obtaining no heads. First, we calculate the probability of obtaining no heads. This can happen if both coins show tails. - Probability of getting a tail with the first coin = \( 1 - 0.25 = 0.75 \) - Probability of getting a tail with the second coin = \( 0.4 \) Thus, the probability of both coins showing tails is: \[ P(\text{both tails}) = 0.75 \times 0.4 = 0.3 \] Therefore, the probability of obtaining at least one head is: \[ P(\text{at least one head}) = 1 - P(\text{both tails}) = 1 - 0.3 = 0.7 \] Thus, the correct answer is \( \frac{7}{10} \).