Multiple choice

In a certain experiment, a biased coin is tossed 80 times. The probability of the coin landing on heads in any single toss is p, where 0 p < 1. What is the probability that the coin lands on heads at least once during these 80 tosses? (1) The probability that the coin lands on tails in a single toss is 0.40. (2) In a large number of tosses, the coin lands on heads approximately 60 percent of the time.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Probability of heads at least once = 1 - P(no heads). P(no heads) = (1-p)^80. Statement (1) says P(tails) = 0.4, so p = 0.6. This is sufficient. Statement (2) says p = 0.6 in the long run, which is also sufficient.

AI explanation

The probability of getting at least one head is found by subtracting the probability of getting all tails from 1. Statement 1 directly provides the probability of tails in a single toss as 0.40, which allows calculating the probability of 80 consecutive tails as (0.40)^80. Statement 2 provides the probability of heads as 0.60, making the probability of tails 0.40, which also allows calculating the required probability. Therefore, each statement alone is sufficient.

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