2. A coin is tossed 3 times. Find the probability of getting (a) Exactly two heads (b) At least two tails

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1. **Determine the sample space:**
   - When a coin is tossed 3 times, each toss has 2 possible outcomes (Head $$ H $$ or Tail $$ T $$).
   - Total number of outcomes is $$2^3 = 8$$.
   - The sample space is:  
     $$
     \{ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT \}
     $$

2. **(a) Exactly Two Heads:**
   - Identify the outcomes with exactly 2 heads.
   - The outcomes with exactly 2 heads are:  
     $$
     \{ HHT, HTH, THH \}
     $$
   - Number of favorable outcomes = 3.
   - The probability is calculated as:  
     $$
     \text{Probability} = \frac{3}{8}
     $$

3. **(b) At Least Two Tails:**
   - Identify the outcomes with at least 2 tails.
   - The outcomes with at least 2 tails are:  
     $$
     \{ TTT, TTH, THT, HTT \}
     $$
   - Number of favorable outcomes = 4.
   - The probability is calculated as:  
     $$
     \text{Probability} = \frac{4}{8} = \frac{1}{2}
     $$
- **(a) Exactly Two Heads:** The probability is $$ \frac{3}{8} $$. - **(b) At Least Two Tails:** The probability is $$ \frac{1}{2} $$.

A coin is tossed 3 times. Find the probability of getting
(a) Exactly two heads
(b) At least two tails

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