Problem 53 - Algebra and Trigonometry

Question

If you toss a fair coin six times, what is the probability of getting all heads?

Step-by-Step Solution

Answer

The probability of getting all heads when tossing a fair coin six times is 1/64.

Step 1: Determine the Probability of One Toss

First, it’s necessary to determine the probability of getting a 'head' in one toss of the fair coin. Since the coin is fair, it means it has two equally likely outcomes - 'head' and 'tail'. Therefore, the probability \(P\) of getting a 'head' in one toss is \(P = 1/2\).

Step 2: Apply the Multiplication Rule of Probability

Since we want to find the probability of getting 'heads' in six tosses, and each toss is an independent event, we can use the multiplication rule for independent events. The multiplication rule states that the probability of occurrence of independent events is equal to the product of their individual probabilities. Hence, the probability of getting all 'heads' is \(P = (1/2) \times (1/2) \times (1/2) \times (1/2) \times (1/2) \times (1/2) = (1/2)^6\).

Step 3: Calculate the Final Probability

Calculating the final result, \(P = (1/2)^6 = 1/64.\) This is the probability of getting all 'heads' in six tosses of the fair coin.