Multiple choice

When two fair coins and 3 cubical dice are thrown simultaneously, the total number of sample points in the sample space is

  1. $2^{2}\times 6^{3}$
  2. $2^{3}\times 6^{2}$
  3. $2^{4}\times 6^{3}$
  4. $2^{3}\times 6^{3}$
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A Correct answer
Explanation

The number of outcomes for one coin is 2, and for one die is 6. For two coins and three dice, the total sample points are 2^2 * 6^3.

AI explanation

By the fundamental principle of counting, the total number of sample points in a sample space is the product of the possible outcomes for each independent event. When two fair coins and three cubical dice are thrown, each coin has 2 outcomes and each die has 6 outcomes. Therefore, the total number of sample points is 2 multiplied by 2 for the coins and 6 multiplied by 6 multiplied by 6 for the dice, resulting in 2^2 x 6^3.

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