To calculate the probability of getting all heads when tossing a fair coin 4 times, we first need to understand the probabilities involved in each individual toss.
A fair coin has two possible outcomes: heads (H) and tails (T). When you toss the coin once, the probability of getting heads is:
- P(H) = 1/2
- P(T) = 1/2
When we toss the coin multiple times, the outcomes are independent of each other. That means the outcome of one toss does not affect the outcome of another toss. Therefore, to find the probability of getting heads in multiple tosses, we multiply the probabilities of getting heads for each toss.
In the case of tossing the coin 4 times, the probability of getting heads in each toss remains 1/2. So, to find the probability of getting heads in all 4 tosses, we calculate:
P(all heads) = P(H) × P(H) × P(H) × P(H)
Substituting in our values:
P(all heads) = (1/2) × (1/2) × (1/2) × (1/2) = (1/2)4
This calculation yields:
P(all heads) = 1/16
Thus, the probability of getting all heads when tossing a coin 4 times is 1/16 or 6.25%.
This means that if you were to toss the coin 4 times repeatedly, you’d expect to get all heads once in every 16 complete sets of tosses on average.