What is the percent of decrease from 300,000 to 30,000? please answer quick.
1 answer:
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Answer:
1.B. No. You need to know the value of P(A and B). 2.C. Yes P(A and B) =0, so P(A or B) = P(A) + P(B).
Step-by-step explanation:
We can solve this question considering the following:
For two mutually exclusive events:
(1)
An extension of the former expression is:
(2)
In <em>mutually exclusive events,</em> P(A and B) = 0, that is, the events are <em>independent </em>one of the other, and we know the probability that <em>both events happen</em> <em>at the same time is zero</em> (P(A <em>and</em> B) = 0). There are some other cases in which if event A happens, event B too, so they are not mutually exclusive because P(A <em>and</em> B) is some number different from zero. Notice the difference between <em>OR</em> and <em>AND. The latter implies that both events happen at the same time.</em>
In other words, notice that the formula (2) provides an extension of formula (1) for those events that are not <em>mutually exclusive</em>, that is, there are some cases in which the events share the same probabilities in a way that these probabilities <em>must be subtracted</em> from the total, so those probabilities in common do not "inflate" the actual probability.
For instance, imagine a person going to a gas station and ask for checking both a tire and lube oil of his/her car. The probability for checking a tire is P(A)=0.16, for checking lube oil is P(B)=0.30, and for both P(A and B) = 0.07.
The number 0.07 represents the probability that <em>both events occur at the same time</em>, so the probability that this person ask for checking a tire or the lube oil of his/her car is:
P(A or B) = 0.16 + 0.30 - 0.07 = 0.39.
That is why we cannot simply add some given probabilities <em>without acknowledging if the events are or not mutually exclusive</em>, whereas we can certainly add the probabilities in question when we know that both probabilities are <em>mutually exclusive</em> since P(A and B) = 0.
In conclusion, knowing the events are mutually exclusive <em>does</em> provide <em>extra information</em> and we can proceed to simply add the probabilities of either event; thus, the answers are those in which <em>we need to previously know the value of P(A and B)</em>.
Answer:
Option (B).
Step-by-step explanation:
From the table shown in the figure attached,
There is a common difference of 5 in every successive and previous term, so the relation is a linear relation.
Let the equation representing the relation is,
y - y' = m(x - x')
where m = slope of the line
Now we choose two ordered pairs from the table,
Let the points are (10, 54) and (11, 59)
Slope =
m =
m = 5
Now the equation of of the line passing through (10, 54) and slope = 5
y - 54 = 5(x - 10)
y - 54 = 5x - 50
y = 5x - 50 + 54
y = 5x + 4
By substituting the values of x and y from the ordered pairs given in the options we find option B satisfies the equation.
For (2, 14),
14 = 5×2 + 4
14 = 14 [True]
For (3, 19),
19 = 5×3 + 4
19 = 19 [True]
Therefore, option (B) will be the answer.