3.5 Coin flips. If you flip a fair coin 10 times, what is the probability of (a) getting all tails? (b) getting all heads? (c) getting at teast one tails?

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Let the total number of outcomes be $$2^{10}$$.

1. To get all tails:
   - There is only 1 favorable outcome.
   - The probability is $$\dfrac{1}{2^{10}} = \dfrac{1}{1024}$$.

2. To get all heads:
   - There is only 1 favorable outcome.
   - The probability is $$\dfrac{1}{2^{10}} = \dfrac{1}{1024}$$.

3. To get at least one tail:
   - First, calculate the probability of getting no tails (i.e., all heads), which is $$\dfrac{1}{1024}$$.
   - Then the probability for at least one tail is:
     $$
     1 - \dfrac{1}{1024} = \dfrac{1023}{1024}
     $$

- The probability of getting all tails is $$ \frac{1}{1024} $$. - The probability of getting all heads is $$ \frac{1}{1024} $$. - The probability of getting at least one tail is $$ \frac{1023}{1024} $$.

3.5 Coin flips. If you flip a fair coin 10 times, what is the probability of (a) getting all tails? (b) getting all heads? (c) getting at teast one tails?

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