Question

7 3 ps-13
each of three friends flips a coin 71 times. the results for each friend are shown in the tables. find the relative frequency for
the event \heads\ for each friend. if the friends combine their results to get 124 heads and 89 tails, what is the relative
frequency for the event \heads\? use pencil and paper. suppose each friend flips a coin 710 times. is there a value you
would expect the relative frequency for the event \heads\ to be close to?

the relative frequency for the event \heads\ for friend 1 is 0.44
(type an integer or a decimal rounded to the nearest hundredth as needed )
the relative frequency for the event \heads\ for friend 2 is 0.62
(type an integer or a decimal rounded to the nearest hundredth as needed )
the relative frequency for the event \heads\ for friend 3 is
(type an integer or a decimal rounded to the nearest hundredth as needed )

Explanation:

Step1: Calculate Friend 3's head relative frequency

Relative frequency = $\frac{\text{Number of heads}}{\text{Total flips}}$ = $\frac{49}{71}$

Step2: Round to nearest hundredth

$\frac{49}{71} \approx 0.69$

Step3: Calculate combined heads relative frequency

Relative frequency = $\frac{\text{Total combined heads}}{\text{Total combined flips}}$ = $\frac{124}{124+89}$ = $\frac{124}{213}$

Step4: Round combined frequency to nearest hundredth

$\frac{124}{213} \approx 0.58$

Step5: Identify expected long-run frequency

For a fair coin, the theoretical probability of heads is $\frac{1}{2} = 0.5$

Answer:

The relative frequency for the event "heads" for Friend 3 is 0.69
The relative frequency for the combined event "heads" is 0.58
You would expect the relative frequency for "heads" to be close to 0.5