Three fair coins are tossed at the same time. What is the probability that one of the coins will show heads and other two will show tails?
To calculate the probability, we need to determine the number of favorable outcomes (getting one head and two tails) and the total number of possible outcomes (all possible outcomes when tossing three coins).
Let's start by finding the total number of possible outcomes when tossing three coins. Since each coin can either show a head or a tail, there are 2 possibilities for each coin. Therefore, the total number of possible outcomes is 2^3, which is 8.
Now let's determine the number of favorable outcomes, which are the outcomes where one coin shows heads and the other two show tails. There are three possible scenarios for this:
1. First coin shows heads, and the other two coins show tails. This can happen in only one way: H (heads) T (tails) T (tails).
2. Second coin shows heads, and the other two coins show tails. This can also happen in one way: T (tails) H (heads) T (tails).
3. Third coin shows heads, and the other two coins show tails. Again, this can happen in one way: T (tails) T (tails) H (heads).
Therefore, the number of favorable outcomes is 3.
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 3 / 8
= 0.375
= 37.5%
Therefore, the probability that one of the coins will show heads and the other two will show tails is 0.375 or 37.5%.