Question

What does it mean to say that the probability that a coin toss will land head side up is \(0.5 ?\)

Short answer

The probability \(0.5\) for a coin toss landing head side up means that there is an equal chance (50%) of the coin landing heads up or tails up. In larger number of tosses, heads would be expected to appear about half the time.

Step-by-step solution

Understand the concept of probability

Probability is a measurement of the likelihood that an event will happen. It is a value between 0 and 1, inclusive. A probability of 1 means the event is certain to happen, a probability of 0 means the event will not happen, and a probability of 0.5 suggests the event is equally likely to happen or not happen.

Apply the concept to the given situation

In the context of a coin toss, there are two possible outcomes: heads or tails. If the coin is fair (i.e., not biased), then each side has an equal chance of appearing. Therefore, the probability is \(0.5\) or 50% for each.

Interpret the probability

To say that the probability that a coin toss will land head side up is \(0.5\) means that, for a large number of coin flips, we would expect heads to appear approximately half of the time. In other words, if the coin is flipped 100 times, we would expect to see about 50 heads. This doesn't mean every 100 flips will produce exactly 50 heads, but rather, this is the expected average over repeated trials.