Mathematics: Trucks that travel on highways have to stop at various locations to be weighed and inspected for safe brakes and light systems. of these trucks, 76% are on interstate commerce while 24% are intrastate. of the intrastate trucks, 3.4% are flagged for safety defects compared to 0.7% of those that are on interstate business. complete parts a through c below. a. calculate the probability that a randomly chosen truck is an interstate truck and is not flagged for a safety violation. the probability is

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Trucks that travel on highways have to stop at

Shu11

03.01.2022

The reuired probability is 0.756

Step-by-step explanation:

Let the number of trucks be 'N'

1) Trucks on interstate highway N'= 76% of N =0.76N

2) Truck on intra-state highway N''= 24% of N = 0.24N

i) Number of trucks flagged on intrastate highway = 3.4% of N'' = $\frac{3.4}{100}\times 0.24N=0.00816N$

ii) Number of trucks flagged on interstate highway = 0.7% of N' = $\frac{0.7}{100}\times 0.76N=0.00532N$

Part a)

The probability that the truck is an interstate truck and is not flagged for safety is $P(E)=P_{1}\times (1-P_{2})$

where

$P_{1}$ is the probability that the truck chosen is on interstate

$P_{2}$ is the probability that the truck chosen on interstate is flagged

$\therefore P(E)=0.76\times (1-0.00532)=0.756$

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