Question

Ellen claims she has a coin that is weighted so that the probability of heads is 70%.

To test this, Ellen flips the coin 100 times and calculates the relative frequency of each outcome.

Outcome Heads Tails
Relative Frequency 0.69 0.31
Which statements about Ellen's experiment are true?

Select each correct answer.

The relative frequency of heads is very different from 70%.

Ellen's claim about the theoretical probability of heads is likely to be false.

The theoretical probability of tails is most likely 30%.

It is likely that the coin is not fair.

Answer 1

Outcome Heads Tails
Relative Frequency 0.69 0.31

so first statement is false as 69% is close to 70%.

second statement is false as heads probability is close to 70%

last 2 statements are true:

The theoretical probability of tails is most likely 30%.

It is likely that the coin is not fair.

Answer 2

• The theoretical probability of tails is most likely 30%.

• It is likely that the coin is not fair.

Explanation:

The table that represents the relative frequency of number of head and tails that are obtained on flipping the coin 100 times is:

Outcome Heads Tails

Relative Frequency 0.69 0.31

Ellen claims she has a coin that is weighted so that the probability of heads is 70%.

Hence, clearly from the table we could see that :

The theoretical probability of tail is 30%.

( Since relative frequency is 0.31 which leads to number of tails as 31 times out of 100 and hence percentage is 31% which is approximately equal to 30%).

Also, it is likely that the coin is not fair.

( Since the coin is turning up to give heads most of the time as compared to tails.

Hence, from the relative frequency we could see that the coin is unfair)