Question
a) If a fair co in is flipped 2 t imes, h ow many times would you e xpect it to land o n tails? b) A coin is flipped 2 time s and lands on ta ils both t imes. Is this en ough evide nce to say t he coin is b iase d? Write a sen tenc e to explain your answ er.
Answer
4
(307 Votes)
Ulric
Elite · Tutor for 8 years
Answer
a) Given the expected number of times. You would expect to get ```tails``` after a fair flip of the coin, about
time.b) No, there's not enough evidence. Getting tails twice in a row is not statistically improbable nor dominate evidence to conclude bias with only a sample size of 2. We cannot make any definite conclusions about a bias in the coin flip. Need more data.
Explanation
## Step1: Identify the number of possible outcomes. When flipping a coin, there are two possibilities: heads or tails; thus the probability of getting a tails in a single flip is
. Therefore, a fair coin being flipped twice would so have this same probability each time.## Step2: Calculating expectation calculation. To calculate the expected number of times an event happens, the probability is multiplied by the number of trials. Here the number of trials is 2 and the probability of each trial is
.### Formula used here:
Calculate by substituting probability and number of trials into the formula.## Step3: For part b, Consider the context of the problem. Two experiments cannot provide sufficient evidence to claim that the coin is biased. Probability of flipping tails or heads 2 times in a row on a fair coin appears as
, which is not an unlikely event. Bias can be statistically supported only with a larger dataset demonstrating a clearer indication of bias.