To find the probability of getting zero heads in five tosses of a fair coin, we start by defining the scenario. For each toss of the coin, there are two possible outcomes: heads (H) or tails (T). Since we want to calculate the probability of getting zero heads, we focus on only getting tails in all five tosses.
The probability of getting tails in a single toss of a fair coin is 0.5 (or 50%). Since each toss is independent, the combined probability of getting tails in all five tosses can be calculated by multiplying the individual probabilities together.
Here is the calculation:
- Probability of tails in 1st toss: 0.5
- Probability of tails in 2nd toss: 0.5
- Probability of tails in 3rd toss: 0.5
- Probability of tails in 4th toss: 0.5
- Probability of tails in 5th toss: 0.5
Now, we multiply these probabilities:
P(0 ext{ heads}) = 0.5 imes 0.5 imes 0.5 imes 0.5 imes 0.5 = (0.5)^5 = rac{1}{32} ext{ or approximately } 0.03125
This means that the probability of getting zero heads when tossing a coin five times is extbf{3.125%}. In other words, out of 32 sets of five coin tosses, we would expect to get all tails in just one of those sets, reflecting a relatively low chance of flipping only tails in five attempts.