Question

A proper unbiased coin was tossed 10 times for 3 trials, giving TTHHTHTTHH, TTTTTHHHHH, and THTHHTHTTH (T = Tails; H = Heads). What is the difference between the theoretical and experimental probabilities of getting heads?

a 0.0

b 0.1

c 0.3

d 0.5

Answer 1

Trial 1:

TTHHTHTTHH

how many heads are in that sequence above?

Answer 2

5

Answer 3

out of 10 tosses total, so the experimental probability of getting heads is 5/10 = 1/2

Answer 4

repeat the same steps for trial 2: TTTTTHHHHH

Answer 5

15 heads for all trials

Answer 6

d would be correct?

Answer 7

there are 5 heads in TTTTTHHHHH out of 10 tosses

so again, experimental probability of getting heads is 5/10 = 1/2

Answer 8

trial 3: THTHHTHTTH

experimental probability of getting heads is equal to what?

Answer 9

1/2

Answer 10

yep since again there are 5 heads out of 10 tosses

Answer 11

each time we got 1/2

theoretically, the probability of getting heads is 1/2 because there are 2 outcomes (heads or tails) and 1 of those outcomes is heads

Answer 12

so in this case, the difference is 0 (ie there is no difference). Usually the experimental probability will be a bit off from the theoretical probability

Answer 13

Okay I understand. I wasn't sure what theoretical probability meant. So the answer would be a.

Answer 14

experimental probability is the probability you record after doing an experiment (or multiple experiments)

theoretical probability is based off the idea that each side has an equal chance of popping up (this is something you can do without doing experiments)

Answer 15

Thank you for helping.

Answer 16

another way to do this:
experimental probability of heads = 15/30
(since there are 15 heads out of a total of 30 tosses).
theoretical probability of heads = 1/2
now subtract the two fractions