A traffic engineer is counting the number of vehicles by type that turn into a residential area. The table below shows the results of the counts during a​ four-hour period. What is the probability that the next vehicle passing is an​ SUV?

Question

Start 8 By 2 Table 1st Row 1st Column Type of vehicle 2nd Column Number 2nd Row 1st Column Car 2nd Column 271 3rd Row 1st Column SUV 2nd Column 411 4st Row 1st Column Van 2nd Column 77 5st Row 1st Column Small truck 2nd Column 269 6st Row 1st Column Large truck 2nd Column 212 7st Row 1st Column Dump truck 2nd Column 21 8st Row 1st Column Other 2nd Column 68 EndTable

Answer 1

To find the probability that the next vehicle passing is an SUV, we first need to calculate the total number of vehicles observed and then determine the proportion of SUVs among them.

From the table, we can see the counts for each type of vehicle:

• Car: 271
• SUV: 411
• Van: 77
• Small truck: 269
• Large truck: 212
• Dump truck: 21
• Other: 68

Now we can calculate the total number of vehicles:

\[ \text{Total vehicles} = 271 + 411 + 77 + 269 + 212 + 21 + 68 \]

Calculating this step by step:

1. \(271 + 411 = 682\)
2. \(682 + 77 = 759\)
3. \(759 + 269 = 1028\)
4. \(1028 + 212 = 1240\)
5. \(1240 + 21 = 1261\)
6. \(1261 + 68 = 1329\)

So, the total number of vehicles is 1329.

Next, we find the number of SUVs, which is 411.

Now we can calculate the probability \(P\) that the next vehicle passing is an SUV:

\[ P(\text{SUV}) = \frac{\text{Number of SUVs}}{\text{Total number of vehicles}} = \frac{411}{1329} \]

To express this as a decimal, we can perform the division:

\[ P(\text{SUV}) \approx 0.309 (rounded to three decimal places) \]

Thus, the probability that the next vehicle passing is an SUV is approximately \(0.309\), or \(30.9%\).