Question

Four fair coins are tossed simultaneously. The probability that at least one tail turns up is:

• A. \(\tfrac{1}{16}\)
• B. \(\tfrac{15}{16}\)
• C. \(\tfrac{7}{8}\)
• D. \(\tfrac{1}{2}\)

Hint:

In probability, for "at least one" type problems, always use the complement rule: \[ P(\text{at least one}) = 1 - P(\text{none}). \] This avoids lengthy counting.

Answer 1

The Correct Option is B

Step 1: Total outcomes.
Each coin has 2 possible outcomes. For 4 coins: \[ \text{Total outcomes} = 2^4 = 16. \] Step 2: Complementary approach.
It is easier to calculate the probability of "no tail" (i.e., all heads). Probability(all heads) = \(\tfrac{1}{16}\). Step 3: At least one tail.
\[ P(\text{at least one tail}) = 1 - P(\text{no tail}) = 1 - \tfrac{1}{16} = \tfrac{15}{16}. \] Final Answer: \[ \boxed{\tfrac{15}{16}} \]