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Question

Part 1
If you toss a fair coin 4 ​times, what is the probability of getting all tails​?

Answer 1

To calculate the probability of getting all tails when tossing a fair coin 4 times, we can follow these steps:

1. Determine the number of outcomes for each toss: A fair coin has 2 possible outcomes (heads or tails).

2. Calculate the total number of outcomes for 4 tosses: For 4 tosses, the total number of outcomes is given by \(2^4\): \[ 2^4 = 16 \]

3. Identify the number of favorable outcomes: There is only 1 favorable outcome for getting all tails (TTTT).

4. Calculate the probability: The probability \(P\) of getting all tails is the ratio of the number of favorable outcomes to the total number of outcomes: \[ P(\text{all tails}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{16} \]

Therefore, the probability of getting all tails when tossing a fair coin 4 times is \(\frac{1}{16}\).