Mathematics, 04.02.2020 05:45 maddy1854

Afire company keeps two rescue vehicles. because of the demand on the vehicles and the chance of mechanical failure, the probability that a specific vehicle is available when needed is 90%. the availability of one vehicle is independent of the availability of the other. find the probability that (a) both vehicles are available at a given time, (b) neither vehicle is available at a given time, and (c) at least one vehicle is available at a given time.

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Answer from: savthespice

(a) P (Both vehicles are available at a given time) = 0.81

(b) P (Neither vehicles are available at a given time) = 0.01

Step-by-step explanation:

Let A = Vehicle 1 is available when needed and B = Vehicle 2 is available when needed.

Given:

The availability of one vehicle is independent of the availability of the other, i.e. P (A ∩ B) = P (A) × P (B)

P (A) = P (B) = 0.90

(a)

Compute the probability that both vehicles are available at a given time as follows:

P (Both vehicles are available) = P (Vehicle 1 is available) ×

P (Vehicle 2 is available)

$P(A\cap B)=P(A)\times P(B)$

$=0.90\times0.90\\=0.81$

Thus, the probability that both vehicles are available at a given time is 0.81.

(b)

Compute the probability that neither vehicles are available at a given time as follows:

P (Neither vehicles are available) = [1 - P (Vehicle 1 is available)] ×

[1 - P (Vehicle 2 is available)]

$P(A^{c}\cap B^{c})=[1-P(A)]\times [1-P(B)]\\$

$=(1-0.90)\times (1-0.90)\\=0.10\times0.10\\=0.01$

Thus, the probability that neither vehicles are available at a given time is 0.01.

(c)

Compute the probability that at least one vehicle is available at a given time as follows:

P (At least one vehicle is available) = 1 - P (None of the vehicles are available)

$=1-[P(A^{c})\times P(B^{c})]\\=1-0.01.....(from\ part\ (b))\\ =0.99$

Thus, the probability that at least one vehicle is available at a given time is 0.99.

Answer from: Quest

answer: true

step-by-step explanation:

Answer from: Quest

I'll do the first one for you. it isn't very hard at all.on number one, you have (50 × 3), which equals 150, and (3 × 3), which equals 9. after you establish that, you add 150 and 9 together. so, (150 + 9) equals 159.this means that 53 × 3 = 159.

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