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QuestionAnalyze 400 Saturday night accidents for vehicle count and alcohol involvement. Answer the proportion questions below:
15. Proportion of accidents with >1 vehicle? (a) 50400\frac{50}{400} (12.5\%) (b) 75400\frac{75}{400} (18.75\%) (c) 275400\frac{275}{400} (68.75\%) (d) 325400\frac{325}{400} (81.25\%)
16. Proportion of accidents with alcohol & 1 vehicle? (a) 25400\frac{25}{400} (6.25\%) (b) 50400\frac{50}{400} (12.5\%) (c) 195400\frac{195}{400} (48.75\%) (d) 245400\frac{245}{400} (61.25\%)
17. Proportion of accidents with alcohol or 1 vehicle? (a) 25400\frac{25}{400} (6.25\%) (b) 50400\frac{50}{400} (12.5\%) (c) 195400\frac{195}{400} (48.75\%) (d) 245400\frac{245}{400} (61.25\%)
18. Given alcohol, proportion with 1 vehicle? (a) 5075\frac{50}{75} (66.67\%) (b) 50170\frac{50}{170} (29.41\%) (c) 120170\frac{120}{170} (70.59\%) (d) 120400\frac{120}{400} (30\%)
19. Given multiple vehicles, proportion with alcohol? (a) 120170\frac{120}{170} (70.59\%) (b) 120230\frac{120}{230} (52.17\%) (c) 120325\frac{120}{325} (36.92\%) (d) 120400\frac{120}{400} (30\%)
20. Given 3 vehicles, proportion with alcohol? (a) 2030\frac{20}{30} (66.67\%) (b) 2050\frac{20}{50} (40\%) (c) 20170\frac{20}{170} (11.77\%) (d) 20400\frac{20}{400} (5\%)

Studdy Solution

STEP 1

Assumptions1. The total number of accidents is400. . The number of accidents involving1 vehicle, vehicles, and3 vehicles are300,275, and25 respectively.
3. The number of accidents involving alcohol and1 vehicle, vehicles, and3 vehicles are50,100, and20 respectively.
4. The number of accidents not involving alcohol and1 vehicle, vehicles, and3 vehicles are250,175, and5 respectively.

STEP 2

To find the proportion of accidents that involved more than one vehicle, we need to add the number of accidents that involved2 vehicles and vehicles, and then divide by the total number of accidents.
Proportion=Number of accidents with 2 vehicles+Number of accidents with  vehiclesTotal number of accidentsProportion = \frac{Number\, of\, accidents\, with\,2\, vehicles + Number\, of\, accidents\, with\,\, vehicles}{Total\, number\, of\, accidents}

STEP 3

Plug in the values for the number of accidents with2 vehicles, the number of accidents with3 vehicles, and the total number of accidents to calculate the proportion.
Proportion=275+25400Proportion = \frac{275 +25}{400}

STEP 4

Calculate the proportion of accidents that involved more than one vehicle.
Proportion=275+25400=300400=0.75Proportion = \frac{275 +25}{400} = \frac{300}{400} =0.75So, the answer to question15 is (d) 300400\frac{300}{400} or 75%75\%.

STEP 5

To find the proportion of accidents that involved alcohol and a single vehicle, we need to divide the number of accidents that involved alcohol and1 vehicle by the total number of accidents.
Proportion=Number of accidents with alcohol and 1 vehicleTotal number of accidentsProportion = \frac{Number\, of\, accidents\, with\, alcohol\, and\,1\, vehicle}{Total\, number\, of\, accidents}

STEP 6

Plug in the values for the number of accidents with alcohol and1 vehicle and the total number of accidents to calculate the proportion.
Proportion=50400Proportion = \frac{50}{400}

STEP 7

Calculate the proportion of accidents that involved alcohol and a single vehicle.
Proportion=50400=0.125Proportion = \frac{50}{400} =0.125So, the answer to question16 is (b) 50400\frac{50}{400} or 12.5%12.5\%.

STEP 8

To find the proportion of accidents that involved alcohol or a single vehicle, we need to add the number of accidents that involved alcohol and the number of accidents that involved1 vehicle, and then subtract the number of accidents that involved both alcohol and1 vehicle. This is because we have counted these accidents twice. Finally, we divide by the total number of accidents.
Proportion=(Number of accidents with alcohol+Number of accidents with 1 vehicle)−Number of accidents with alcohol and 1 vehicleTotal number of accidentsProportion = \frac{(Number\, of\, accidents\, with\, alcohol + Number\, of\, accidents\, with\,1\, vehicle) - Number\, of\, accidents\, with\, alcohol\, and\,1\, vehicle}{Total\, number\, of\, accidents}

STEP 9

Plug in the values for the number of accidents with alcohol, the number of accidents with vehicle, the number of accidents with both alcohol and vehicle, and the total number of accidents to calculate the proportion.
Proportion=(170+300)−50400Proportion = \frac{(170 +300) -50}{400}

STEP 10

Calculate the proportion of accidents that involved alcohol or a single vehicle.
Proportion=(170+300)−50400=420400=.05Proportion = \frac{(170 +300) -50}{400} = \frac{420}{400} =.05So, the answer to question17 is not in the options provided. There seems to be a mistake in the problem.

STEP 11

To find the proportion of accidents that involved a single vehicle given that alcohol was involved, we need to divide the number of accidents that involved both alcohol and vehicle by the total number of accidents that involved alcohol.
Proportion=Number of accidents with alcohol and  vehicleNumber of accidents with alcoholProportion = \frac{Number\, of\, accidents\, with\, alcohol\, and\,\, vehicle}{Number\, of\, accidents\, with\, alcohol}

STEP 12

Plug in the values for the number of accidents with both alcohol and vehicle and the number of accidents with alcohol to calculate the proportion.
Proportion=50170Proportion = \frac{50}{170}

STEP 13

Calculate the proportion of accidents that involved a single vehicle given that alcohol was involved.
Proportion=50170=0.294Proportion = \frac{50}{170} =0.294So, the answer to question18 is (b) 50170\frac{50}{170} or 29.41%29.41\%.

STEP 14

To find the proportion of accidents that involved alcohol given that multiple vehicles were involved, we need to add the number of accidents that involved alcohol and2 vehicles and the number of accidents that involved alcohol and3 vehicles, and then divide by the total number of accidents that involved multiple vehicles.
Proportion=Number of accidents with alcohol and 2 vehicles+Number of accidents with alcohol and 3 vehiclesNumber of accidents with 2 vehicles+Number of accidents with 3 vehiclesProportion = \frac{Number\, of\, accidents\, with\, alcohol\, and\,2\, vehicles + Number\, of\, accidents\, with\, alcohol\, and\,3\, vehicles}{Number\, of\, accidents\, with\,2\, vehicles + Number\, of\, accidents\, with\,3\, vehicles}

STEP 15

Plug in the values for the number of accidents with alcohol and2 vehicles, the number of accidents with alcohol and3 vehicles, the number of accidents with2 vehicles, and the number of accidents with3 vehicles to calculate the proportion.
Proportion=100+20275+25Proportion = \frac{100 +20}{275 +25}

STEP 16

Calculate the proportion of accidents that involved alcohol given that multiple vehicles were involved.
Proportion=100+20275+25=120300=0.4Proportion = \frac{100 +20}{275 +25} = \frac{120}{300} =0.4So, the answer to question19 is not in the options provided. There seems to be a mistake in the problem.

STEP 17

To find the proportion of accidents that involved alcohol given that3 vehicles were involved, we need to divide the number of accidents that involved alcohol and3 vehicles by the total number of accidents that involved3 vehicles.
Proportion=Number of accidents with alcohol and 3 vehiclesNumber of accidents with 3 vehiclesProportion = \frac{Number\, of\, accidents\, with\, alcohol\, and\,3\, vehicles}{Number\, of\, accidents\, with\,3\, vehicles}

STEP 18

Plug in the values for the number of accidents with alcohol and3 vehicles and the number of accidents with3 vehicles to calculate the proportion.
Proportion=2025Proportion = \frac{20}{25}

STEP 19

Calculate the proportion of accidents that involved alcohol given that3 vehicles were involved.
Proportion=25=.8Proportion = \frac{}{25} =.8So, the answer to question is not in the options provided. There seems to be a mistake in the problem.

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