Problem 54 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The probability of getting all tails when tossing a fair coin seven times is 0.008.

Step 1: Determine the Probability of Single Event

Each toss of a fair coin has two possible outcomes, heads (H) or tails (T), which are equally probable. Then the probability of getting a tail in a single toss is \(\frac{1}{2}\).

Step 2: Determine the Probability of Multiple Independent Events

With independent events, the probability of each event is not influenced by the occurrence of the other events. To find the combined probability of independent events, we multiply the probabilities of the individual events. The question asks for the probability of getting seven tails (T) in seven independent tosses. Therefore, to find this probability, we multiply the probability of getting a tail in a single toss, \(\frac{1}{2}\), by itself seven times, which can be written as \(\left(\frac{1}{2}\right)^7\).

Step 3: Calculate the Probability

'Perseverance required to calculate \(\left(\frac{1}{2}\right)^7\), the result is \(0.0078125\) or approximately \(0.008\) when rounded to three decimal places.