# In a random experiment, a symmetric coin is thrown four times. Find the probability that the eagle will fall exactly 3 times.

To find the Probability of any event, you need to determine the number of all possible options for the event and the number of event options that interest us.

All event options 2 * 2 * 2 * 2 = 16

To better understand this, consider the simpler options:

If a coin were thrown only once, then there would be 2 options (heads or tails).

If a coin were thrown twice, then there would be 2 * 2 options (heads or tails) * (heads or tails).

If a coin were thrown three times, then there would be 2 * 2 * 2 options (heads or tails) * (heads or tails) * (heads or tails).

If a coin is thrown four times, then 2 * 2 * 2 * 2 options (heads or tails) * (heads or tails) * (heads or tails) * (heads or tails).

Now we find how many options when the eagle drops exactly 3 times:

1. When the eagle falls on the first, second and third throw.

2. When the eagle falls on the first, second and fourth throw.

3. When the eagle falls on the first, third and fourth throw.

4. When the eagle falls on the second, third and fourth throw.

Total 4 options, then:

P = 4/16 = 1/4 = 0.25

Answer: 0.25