There are many ways to attack a probability question, but two ways are most common to attack most probability questions. A) You calculate with P(A) = 1 - P(nA) or B) P(nA) directly.
The following example will show what I mean.
A fair six-sided dice with faces numbered one through six rolled three times. What is the probability that the face with the number 6 on it will NOT be facing upward on all three rolls?
Use P(A) = 1 - P ---> P(6) = 1/6 x 3 rolls = 1/216 ---> Use P(A) = 1 - P AGAIN P(A) = 1 - P ---> 1 - 1/216 = 215/216
P(n6) = 5/6 x 3 rolls = 125/216
Since only one solution is correct and I repeatedly stumble over this very easy issue, I would like to ask the experts how to identify when to use which solution. Anyone any idea? It bugs me to screw up on such easy problems. Thanks so much!
Either method can be correct depending on the wording of the question. Here, the wording suggests that Solution A is correct.
Read the question carefully:
What is the probability that the face with the number 6 on it will NOT be facing upward on all three rolls? (You want the probability that you should not get a 6 on all three throws. Getting a 6 on 2 of the 3 throws is acceptable. Getting a 6 on 1 of the 3 throws is also acceptable. But you should not have a 6 on all 3 throws.
Solution A is correct since it finds the probability of getting a 6 on all 3 throws and subtracts it from 1.
Solution B finds the probability of getting no 6. What about the cases in which you get a 6 on only 1 or 2 throws? If you try to solve this question using this method, it will be complicated. You need to adjust for one 6 and then two 6s.
Let's change the question a little:
What is the probability that the face with the number 6 on it will not be facing upwards on any of the three rolls? (Now you don't want 6 to appear an any roll)
Now your Solution B is correct.
So how do you decide which method to use? In each question, try to figure out what exactly do they want. Then think which method will be easier. Is it easier to find P(A) or is it easier to find 1 - P(A). Use whichever method seems more straight forward. Of course some practice will be needed since there are no clear cut rules that will help you decide.
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