Problem 49
Question
If you toss a fair coin six times, what is the probability of getting all heads?
Step-by-Step Solution
Verified Answer
The probability of getting all heads when tossing a fair coin six times is 0.015625.
1Step 1: Understand the Problem
First, it is important to know that the coin is fair, which means the likelihood of landing heads (H) or tails (T) is the same. Second, the coin is tossed six times, and we are asked to find the probability of getting all heads (HHHHHH).
2Step 2: Determine the Probability of a Single Event
For a fair coin, the probability of landing heads (H) is 0.5. Since each event is independent, the probability of multiple events happening is simply the product of the probability of each event.
3Step 3: Calculate the Probability of All Events
Since there are 6 events (coin flips), and each has a 0.5 probability of happening, we simply need to calculate \(0.5^6 = 0.015625\). This is the likelihood of all six coin flips landing heads.
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