Respuesta :
The probability that a single coin toss results in heads is 1/2, and the probability that it results in tails is the same.
To find the theoretical probability of a particular result when two coin tosses are made, multiply the probabilities of the two outputs.
1) Two heads
Since the probability that a coin toss results in heads is 1/2, then the probability that two coin tosses result in two heads is:
[tex]\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}[/tex]3) Two tails
This case is similar to the case of two heads. The probability that two coin tosses result in two heads, is:
[tex]\frac{1}{4}[/tex]5) One head and one tail.
It doesn't matter which appears first, if a head or a tail. Then, there are two different ways in which two coin tosses resulting in one head and one tail can occur: Resulting heads first and tails next, or showing tails first and heads next.
In both cases, the probability of that situation happening is 1/4, so the total theoretical probability that the coin toss results in one head and one tail, is:
[tex]\frac{1}{4}+\frac{1}{4}=\frac{1}{2}[/tex]2, 4, 6)
The experimental probabilities of obtaining two heads, two tails or one of each were:
Two heads: 24/100
Two tails: 44/100
One of each: 32/100
7)
Theoretical probabilities may differ from experimental probabilities because the particular result of a coin toss cannot be predicted. Instead, what theoretical probability tells us is that if we increase the number of repetitions of the experiment, the probability of each different result will approach the theoretical probabilities.
If experimental probabilities do not approach theoretical probabilities, then it is possible that the theoretical probability of each event was not what we thought it was: the probability of the coin toss resulting in tails may be actually greater.
If the number of experiments is small, it is harder for us to distinguish if the discrepancy is due to an experimental fluctuation or if there is a physical reason behind the atypical behavior.
