An insurance company determines that the number of claims received in a week follows a Poisson distribution. The probability that the insurance company receives at most one claim in a week is 5/13 times the probability that the insurance company receives at most two claims in a week. Calculate the probability that

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An insurance company determines that the number of claims received in a week follows a Poisson distribution. The probability that the insurance company receives at most one claim in a week is 5/13 times the probability that the insurance company receives at most two claims in a week.

Calculate the probability that the insurance company receives four claims in a week.

the probability that the insurance company receives four claims in a week is 0.1954

Step-by-step explanation:

P(at most one claim) = P(X ≤ 1)

and

P(at most two claims) = P(X ≤ 2)

for P(X ≤ 1) = (5/13) × P(X ≤ 2)  

P(X ≤ 1 ) = (5/13) × (P(X ≤ 1) + P(X = 2))

(8/13) × P(X ≤ 1) = (5/13) × P(X = 2)

8 × ( e^(-λ) λ⁰ / 0! + e^(-λ)λ₁/1! ) = 5 × (e^(-λ)λ²/2!

16( 1 + λ ) = 5 × λ²

5 × λ²- 16 × λ - 16 = 0

λ = 4

Therefore the probability that the insurance company receives four claims in a week is P(X = 4) =e⁻⁴4⁴/4! = 0.1954

whatvare the choices

step-by-step explanation:

step-by-step explanation:

a cube has 6 sides

the probability of getting 5 on the first cube is 1/6 since only one side of the cube has 5 on it.

there are 3 sides of the cube with even number on it [2,4,6]

therefore the probability of getting even number is 3/6

for both events to happen together, the probability would be

1/6 x 3/6 = 12/36

which simplifies to 1/12