Multiple choice

A coin is tossed 3 times Quantity A The number of possible outcomes containing exactly 2 heads Quantity B The number of possible outcomes containing exactly 1 tail

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Outcomes for 3 tosses: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Exactly 2 heads: HHT, HTH, THH (3 outcomes). Exactly 1 tail: HHT, HTH, THH (3 outcomes). Both are 3.

AI explanation

When a coin is tossed 3 times, the total number of possible outcomes in the sample space is 2 cubed, which is 8. Using the combinations formula, the number of outcomes with exactly 2 heads is 3 choose 2, which equals 3. Similarly, the number of outcomes with exactly 1 tail is also finding 2 heads in 3 tosses, so it is 3 choose 1, which equals 3. Because both quantities evaluate to 3, the two quantities are equal.

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