Q1. If 1 = defective.
1a p(11) = 2/4x1/3 = 1/6
1b p(101 or 011) = 2/4x2/3x1/2x2 = 1/3
1c 1- (1a + 1b) = 1 - (1/6 + 1/3) = 1/2
Q2 The information given yields (for a population of 400): n(U and T)=57;
n(NotU and T)=120; n(U and NotT)=3 where U = 'upper class' and T =
TV-owning. The above can be seen to give: a 6/17 b 177/400 c 19/59
Q3 The problem is essentially p(> 25 connections / minute). If we consider a
connection as the start of a call and a 'rush hour' as precisely 1 hour,
then the probability can be calculated using a Poisson distribution, mean
500/60 = 8.33 ..... which yields probability zero (Am I missing something?)
What if there were 26 calls at 1-second intervals, each lasting for less
than 1 second? Would this overtax the board? ... and so on!
I hope this is of some use
Andre Francis
On 7 February 2011 15:36, marina garcia <[log in to unmask]> wrote:
> hi allstat,
>
> pls kindly help me with these probability problems:
>
> 1. Two defective tubes got mixed up with two good ones. The tubes
> are tested one by one until both defectives are found.
>
> a)What is the probability that both defectives have been found by
> the second test?
> b)What is the probability that three tests are required?
> c)What is the probability that four tests are required?
>
> 2. In a certain city, 15% of the households are classified as being
> of the “upper class”, according to socio-economic criteria. In
> addition, it is known that 95% of upper-class households own
> colored television sets. It is known that 30% of households that
> are not of upper-class status own a TV set. If a sample household
> is to be selected for interview such that all the households of
> the city are equally likely to be selected, find the probability
> that
> a) it does not belong to the upper class but owns a colored
> television set.
> b) it owns a colored television set.
> c) it belongs to the upper class, given that it owns a TV set.
>
> 3. A telephone switchboard handles 500 calls, on an average, during a
> rush hour. The board can make a maximum of 25 connections per
> minute. Evaluate the probability that the board will be overtaxed
> during any given minute.
>
>
> pls pm me the solutions or links to problems similar to the given
> above, if possible, with solutions...
>
> your help is highly appreciated...thanks a lot
>
> marina garcia
> uplb, philippines
>
>
>
>
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