Question

The probability of tossing heads with a standard coin is 1/2, because it is one of two possible outcomes. The probability of tossing three heads in a row is (1/2) ^3 or 1/8
a) What is the probability of tossing 6 heads in a row? Write as a simplified fraction.

b) What is the probability of tossing 12 heads in a row? Write as a simplified fraction.

Answer 1

Answer:

  a) 1/64

  b) 1/4096

Step-by-step explanation:

As you can tell from the example, the exponent of 1/2 is the number of heads in a row.

a) p(6 heads in a row) = (1/2)^6 = 1/(2^6) = 1/64

b) p(12 heads in a row) = (1/2)^12 = 1/(2^12) = 1/4096

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Additional comment

The probability of a head is 1/2 because we generally are concerned with a "fair coin." That is defined as a coin in which each of the 2 possible outcomes has the same probability, 1/2. Similarly, a "fair number cube" has 6 faces, and the probability of each is defined to be the same as any other, 1/6. Loaded dice and unfair coins do sometimes show up in probability problems.