probability問題(急)

2007-03-22 4:53 pm
A,B.C.and D are events! P(A)=0.15 P(B)=0.3 P(C)=0.55 P(D)= 0.80

why (D) is most likely event?
why (A) is least likely event?
why (A) is most predictable event ?
why (C) is least predictable event ?

請詳細地每題解釋答案!!!thx

回答 (3)

2007-03-22 5:04 pm
✔ 最佳答案
Because (D)'s probability is the greatest , so it is more like to happen than the others.

Because (A)'s probability is the smallest , so it is the least likely to happen .

But I think (A) is not the most predictable event and (C) is not the least predictable event
because their probabilities are not suitable to this condition
參考: ME
2007-03-22 5:19 pm
(D) is most likely event because the probability of occurence of event D is 0.8 which
is the LARGEST probability among all the events. In other words, event D
is most likely to happen.

(A) is least likely event because the probability of occurence of event A is 0.15 which
is the SMALLEST probability among all the events. In other words, event A
is least likely to happen.

For question 3 and 4, we need a little bit explanation before answering the question.
The closer the value of probability to 0.5, the more unpredictable that event will be.
This is because 0.5 probability event is the MOST unpredictable event.
If the probability of occurence of event X is 0.5, then the probability that
event X will happen and NOT happen both equal to 0.5. This implies that
event X is EQUALLY likely to happen and NOT happen. In this case, we are NOT
sure whether event X will happen or not happen and event X become most unpredictable.

In conclusion, the closer the probability to 0.5, the more unpredictable that event will be.
Or the closer the probability to 0.5, the less predictable that event will be.
In other words, the further away the probability from 0.5, the more predictable that event will be.

The difference between each of the 4 events to 0.5 is as below:

| 0.5 - P(A)| = |0.5 - 0.15| = 0.35
| 0.5 - P(B)| = |0.5 - 0.30| = 0.20
| 0.5 - P(C)| = |0.5 - 0.55| = 0.05
| 0.5 - P(D)| = |0.5 - 0.80| = 0.30

Now, we have sufficient knowledge to answer question 3 and 4.

From the calculations shown above, we can see that | 0.5 - P(A)| is the largest
value. In other words, P(A) is most far from 0.5 and event A is the most predictable event.

Similary, we can see that | 0.5 - P(C)| is the smallest
value. In other words, P(C) is closest to 0.5 and event C is the least predictable event.
2007-03-22 5:16 pm
A,B.C.and D are events! P(A)=0.15 P(B)=0.3 P(C)=0.55 P(D)= 0.80

why (D) is most likely event?
D is the most likely event because P(D) is the largest meaning 80% of chance that D will happen.
why (A) is least likely event?
A is the least likely event because P(A) is the smallest meaning 15% of chance that A will happen.
why (A) is most predictable event ?
A is the most predicatable event because 85% sure that A will not happen.
why (C) is least predictable event ?
C is the least predictable event because only 55% sure that C will happen.
For B and D, it is 70% sure that B will not happen and 80% sure that D will happen.


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