Help with Poisson distribution question? Watch

theeetimdoherty
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#1
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#1
The question is essentially this:

X~Po(0.8) and Y~Po(1.2)

Find the probability that at least 1 of both both events X and Y during the period.

I worked in out with
P(X≥1) × P(Y≥1) = (1 - P(X=0)) × (1 - P(Y=0))
= (1 - 0.449329) × (1 - 0.301194)
= 0.550671 × 0.6988057
= 0.3848

I believe that's the correct answer however the textbook gives the answer as 0.5947.

Did I go wrong somewhere or is the textbook just wrong?
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timif1
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Can you write the Q properly and I might be able to help
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theeetimdoherty
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During a weekday, cars pass a census point on a quiet side road independently and at random times. The mean rate for westward travelling cars is two in any five-minute period, and for eastward travelling cars is
three in any five-minute period.
Find the probability that at least one car from each direction will pass the census point in a given two-minute period.
(Original post by timif1)
Can you write the Q properly and I might be able to help
I took westward as X and eastward as Y.
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timif1
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Have you heard of joining poison distributions together? You do further maths right? See if you can solve it when you join the distributions.

It’s quite weird tho I got 0.59399...
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theeetimdoherty
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Was it really that easy?

I thought you couldn't combine the poissons because the question says "1 car come from each directions".
I thought that the use of the word "each" instead of "either" makes it specifically that at least one car comes from both directions, as opposed to just being any of the directions.
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Klara_b155
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^I got 0.3848 too - I don't understand why you combine it in this instance
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timif1
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Text book probably wrong
(Original post by Klara_b155)
^I got 0.3848 too - I don't understand why you combine it in this instance
Textbook probably wrong
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