Question Video: Applications of the Counting Principle (Product Rule with Replacement) | Nagwa Question Video: Applications of the Counting Principle (Product Rule with Replacement) | Nagwa

Question Video: Applications of the Counting Principle (Product Rule with Replacement) Mathematics • Second Year of Secondary School

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Use the fundamental counting principle to find the total number of outcomes of tossing 11 coins.

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Video Transcript

Use the fundamental counting principle to find the total number of outcomes of tossing 11 coins.

The fundamental counting principle is a method we can use to find the number of all possible outcomes in a sample space. It tells us that if we have two independent events 𝐴 and 𝐵 such that the number of possible outcomes for event 𝐴 is 𝑥 and the number of possible outcomes for event 𝐵 is 𝑦, then the total number of distinct possible outcomes of the two events together is their product 𝑥 multiplied by 𝑦. This can be extended to any number of independent events. To find the total number of outcomes for all events together, we find the product of the number of outcomes for each individual event.

In this problem, we have 11 coins which are being flipped. Flips of a coin are independent. And so we can calculate the total number of outcomes by considering how many outcomes there are for each coin and then finding the product of these 11 values. Well, each coin has two faces, which usually show either heads or tails. So the number of possible outcomes for each coin is two. This is the same for every coin. So the total number of outcomes with this experiment is two multiplied together 11 times, which we can write as two to the 11th power or two to the power of 11. Starting with two and then doubling this value repeatedly, we can calculate that two to the 11th power is equal to 2,048.

So by applying the fundamental counting principle, we found the total number of outcomes of tossing 11 coins is 2,048.

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