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which table is a probability distribution table?

photo is attached.

Hi!

in a probability table, the x represents a given event, and p is the probability of such event.

There are two rules if you have n events; then p₁ + p₂ + ... + pₙ = 1, this is because the probability is normalized.

whit this info you can discard the third option, because there is a probability bigger than 1, and then the addition of al the probabilities is bigger than 1.

The second rule is that there do not exist negative probabilities (because they don't have sense) then you can also discard the second option.

Now we need to check the first and the fourth options, we need to add the 4 probabilites in each and see if the result is 1.

for the first options we have :  

0.2 + 0.35 + 0.15 + 0.25 = 0.95

this is not normalized, this is not a probability distribution table.

for the fourth option we have:

0.4 + 0.15 + 0.25 + 0.2 = 1

this is normalized, then this is a probability distribution table.

Then the only right answer is option 4.

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: