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2 answers:
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Answer:
Step-by-step explanation:
Given that in a group of 40 people, 35% have never been abroad. Two people are selected at random without replacement and are asked about their past travel experience.
Since the two are drawn without replacement the first trial affects the second trial. In other words, each trial is not independent of the other.
a) Hence this cannot be binomial experiment. The reason is p=probability for each trial is not constant as first draw affect the probability for Ii draw
b) The probability that in a random sample of 2, no one has been abroad
=Prob of selecting both people from the group where no one has been abroad
We have in the group 35% i.e. 14 people never been to abroad
So required probability = Prob of selecting both from 14 people
=
Answer:
Step-by-step explanation:
Given:
u = 1, 0, -4
In unit vector notation,
u = i + 0j - 4k
Now, to get all unit vectors that are orthogonal to vector u, remember that two vectors are orthogonal if their dot product is zero.
If v = v₁ i + v₂ j + v₃ k is one of those vectors that are orthogonal to u, then
u. v = 0 [<em>substitute for the values of u and v</em>]
=> (i + 0j - 4k) . (v₁ i + v₂ j + v₃ k) = 0 [<em>simplify</em>]
=> v₁ + 0 - 4v₃ = 0
=> v₁ = 4v₃
Plug in the value of v₁ = 4v₃ into vector v as follows
v = 4v₃ i + v₂ j + v₃ k -------------(i)
Equation (i) is the generalized form of all vectors that will be orthogonal to vector u
Now,
Get the generalized unit vector by dividing the equation (i) by the magnitude of the generalized vector form. i.e
Where;
|v| =
|v| =
=
This is the general form of all unit vectors that are orthogonal to vector u
where v₂ and v₃ are non-zero arbitrary real numbers.