Question

A fair coin is flipped 10 times. If the first 9 flips resulted in Heads, what is the chance the tenth flip will result in Heads? Make sure your answer is in decimal form.

Answer 1

Answer: Experimental Probability 1.0, Theoretical Probability 0.5

Explanation:

Theoretical Probability is the likeliness of an event occurring.

Experimental Probability is the likeliness of an event occurring based on the previous results.

Since it is a fair coin, there is a half chance the coin lands on heads.
`(1)/(2)` converted to a decimal is 0.5, so therefore that is the theoretical probability.

We are given the previous 9 results as heads. Since this is a fair coin, the chances of that happening is
`((1)/(2)) ^(9)` or
`(1)/(512)`. But that information isn't important. Since we have our first 9 results as heads, the is a 100% chance the next one will be heads based on plainly our previous results.
`(9)/(9)` attempts were heads, and
`(9)/(9)` in decimal form is 1.0, which is our experimental probability.

Hope that helped a lot.

:)

Answer 2

the chance that the tenth flip will result in heads is 0.5 or 50% (in decimal form).

Explanation:

The outcome of each coin flip is independent of the previous flips. In this case, since a fair coin is flipped, the probability of getting heads or tails on each flip is always 0.5 (or 50%).

Even though the first 9 flips resulted in heads, the probability of getting heads on the tenth flip is still 0.5 (50%). The previous flips do not affect the outcome of the next flip because each flip is statistically independent.

i hope this helps! if you have any further questions feel free to ask!