Police plan to enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated 40%, 30%, 20%, and 30% of the time. If a person who is speeding on their way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that they will receive a speeding ticket?

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windyyork windyyork · Answer 1 · 2019-11-05T06:01:15+01:00

Answer: Our required probability is 0.27.

Step-by-step explanation:

Since we have given that

Probability of getting L₁ = 40% = 0.40

Probability of getting L₂ = 30% = 0.30

Probability of getting L₃ = 20% = 0.20

Probability of getting L₄ = 30% = 0.30

Probability that a person is speeding on their way to work at L₁ = 0.2

Probability that a person is speeding on their way to work at L₂ = 0.1

Probability that a person is speeding on their way to work at L₃ = 0.5

Probability that a person is speeding on their way to work at L₄ = 0.2

so, Probability that they will receive a speeding ticket is given by

[tex]0.4\times 0.2+0.3\times 0.1+0.2\times 0.5+0.3\times 0.2\\\\=0.27[/tex]

Hence, our required probability is 0.27.