You are given the information that P(A) = 0.30 and P(B) = 0.40. (1) Do you have enough information to compute P(A or B)? Explai

Question

You are given the information that P(A) = 0.30 and P(B) = 0.40.

(1) Do you have enough information to compute P(A or B)? Explain.

(A) Yes. This probability is equal to 0.70.
(B) No. You need to know the value of P(A and B).
(C) No. You need to know the value of P(A) + P(B).
(D) No. You need to know the value of P(A) – P(B).

(2) If you know that events A and B are mutually exclusive, do you have enough information to compute P(A or B)? Explain.

(A) No. Knowing the events are mutually exclusive does not provide any extra information.
(B) Yes. P(A and B) = 0, so P(A or B) = P(B) – P(A).
(C) Yes. P(A and B) = 0, so P(A or B) = P(A) + P(B).
(D) Yes. P(A and B) = 0.12, so P(A or B) = P(A) + P(B) – 0.12.

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Adalynn 3 weeks 2021-12-27T08:55:28+00:00 1 Answer 0 views 0

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    2021-12-27T08:57:02+00:00

    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:

     \\ A_{1}\;and\;A_{2}

     \\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2}) (1)

    An extension of the former expression is:

     \\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2}) - P(A_{1} and A_{2}) (2)

    In mutually exclusive events, P(A and B) = 0, that is, the events are independent one of the other, and we know the probability that both events happen at the same time is zero (P(A and 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 and B) is some number different from zero. Notice the difference between OR and AND. The latter implies that both events happen at the same time.

    In other words, notice that the formula (2) provides an extension of formula (1) for those events that are not mutually exclusive, that is, there are some cases in which the events share the same probabilities in a way that these probabilities must be subtracted 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 both events occur at the same time, 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 without acknowledging if the events are or not mutually exclusive, whereas we can certainly add the probabilities in question when we know that both probabilities are mutually exclusive since P(A and B) = 0.

    In conclusion, knowing the events are mutually exclusive does provide extra information and we can proceed to simply add the probabilities of either event; thus, the answers are those in which we need to previously know the value of P(A and B).  

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