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Problem 10

# Exercises $$7-12$$ are based on the following table, which shows the frequency of outcomes when two distinguishable coins were tossed 4,000 times and the uppermost faces were observed. $$\begin{array}{|r|c|c|c|c|} \hline \text { Outcome } & \text { HH } & \text { HT } & \text { TH } & \text { TT } \\ \hline \text { Frequency } & 1,100 & 950 & 1,200 & 750 \\ \hline \end{array}$$ What is the relative frequency that the first coin lands with heads up?

Expert verified
The relative frequency of the first coin landing heads up is 0.5125 or 51.25%.
See the step by step solution

## Step 1: Identify the relevant outcomes

We need to find the frequency of the outcomes where the first coin has its heads side up. Looking at the table, we can identify two such outcomes: HH and HT.

## Step 2: Calculate the sum of the relevant frequencies

Now we need to add the frequencies of these two outcomes together. According to the table, HH occurs 1,100 times and HT occurs 950 times. So, the total frequency of the first coin landing heads up is: $$1,100 + 950 = 2,050$$

## Step 3: Calculate the total number of tosses

As per the information given in the exercise, the total number of tosses is 4,000.

## Step 4: Calculate the relative frequency

Finally, we need to divide the sum of the relevant frequencies (2,050) by the total number of tosses (4,000) to find the relative frequency of the first coin landing heads up: $$\frac{2,050}{4,000} = 0.5125$$ So, the relative frequency of the first coin landing heads up is 0.5125 or 51.25%.

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