chetan2u wrote:
Michael KC Chen wrote:
Hi Bunuel
I was wondering why the order of the selection matters here ?
Thanks
Bunuel wrote:
Official Solution:
What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?
(The numbers are selected independently of each other, i.e. they can be equal)
A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20
Prime integers: 23 and 29. Multiples of 3: 21, 24, and 27.
The probability that the first number is prime while the second is a multiple of \(3 = \frac{2}{10} \frac{3}{10} = 0.06\).
The probability that the first number is a multiple of 3 while the second is prime \(= \frac{3}{10} \frac{2}{10} = 0.06\).
The probability that one of the two integers is prime and the other is a multiple of \(3 = 0.06 + 0.06 = 0.12\).
Answer: B
Hi,
more than often follow this rule if in doubt..1) If you are picking two simultaneously/together, you do not have any order in place..
2) whenever you are picking two with/ without repetition, it can be picked as either A and B or B and A..
It's not actually like that. Check this thread (
probability-of-simultaneous-events-veritas-vs-mgat-105994-20.html)
Picking simultaneously is the same as picking one by one without replacement. In any case you need to multiply by the possible number of combinations.
The only case, when you don't need to multiply is when the order is strictly set - for instance, what's the probability that the FIRST number will be prime and the second will be a multiple of 3.