A fair coin is tossed 3 times. Find the probability of obtaining exactly 2 heads.
Answer Details
When a fair coin is tossed once, there are two possible outcomes, either heads or tails. Therefore, the probability of obtaining heads is \(\frac{1}{2}\) and the probability of obtaining tails is also \(\frac{1}{2}\).
Now, when a fair coin is tossed 3 times, there are \(2^3 = 8\) possible outcomes as each toss has 2 possible outcomes (heads or tails). These 8 possible outcomes are:
HHH, HHT, HTH, THH, HTT, THT, TTH, TTT
Out of these 8 outcomes, we need to find the probability of obtaining exactly 2 heads.
We can count the number of outcomes in which exactly 2 heads are obtained as follows:
- HHT
- HTH
- THH
Therefore, there are 3 outcomes in which exactly 2 heads are obtained. So, the probability of obtaining exactly 2 heads is:
\[\frac{\text{number of outcomes in which exactly 2 heads are obtained}}{\text{total number of possible outcomes}} = \frac{3}{8}\]
Hence, the answer is \(\frac{3}{8}\).