What is the size of the sample space when a coin is tossed 5 times in a row?

by

When you toss a coin, there are two possible outcomes for each toss: heads (H) or tails (T). To determine the size of the sample space when the coin is tossed 5 times in a row, we can use the concept of permutations.

For each toss of the coin, there are 2 outcomes. Since the coin is tossed 5 times, we will calculate the total number of outcomes by raising the number of outcomes per toss (2) to the power of the number of tosses (5).

Mathematically, this can be expressed as:

Size of sample space = 2n

where n is the number of tosses. Therefore:

Size of sample space = 25 = 32

This means that if you toss a coin 5 times in a row, there are a total of 32 different possible outcomes in the sample space. Some examples of these outcomes include:

  • HHHHH
  • HHHHT
  • HHHTH
  • HHTHH
  • HTHHH
  • THHHH
  • TTTTT

In summary, the sample space consists of all the possible combinations of heads and tails that can occur through 5 coin tosses, and its size is 32.

Leave a Comment