I hope this helps you
A ) 7 less than triple a number
B ) 7 more than triple a number
C ) 3 less than seven time a number
D ) 3 more than seven time a number
answer is B
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Answer:
9
Step-by-step explanation:
Answer:
The probability that the three friends will meet in the same group is
.
Step-by-step explanation:
We can define the following random variable:
"The friend was assign to the ith group"
This way
and let's define
. This way
and the pdf for
is given by:
![P(Y_i=k) = {3 \choose k}(\frac{1}{600})^{k}(1 - \frac{1}{600} )^{3 - k} \text{ , } k \leq 3](https://tex.z-dn.net/?f=P%28Y_i%3Dk%29%20%3D%20%7B3%20%5Cchoose%20k%7D%28%5Cfrac%7B1%7D%7B600%7D%29%5E%7Bk%7D%281%20-%20%5Cfrac%7B1%7D%7B600%7D%20%29%5E%7B3%20-%20k%7D%20%5Ctext%7B%20%2C%20%7D%20k%20%5Cleq%203)
We want that the three friends stay in the same group, in other words
,
![P(Y_i=3) = {3 \choose 3}(\frac{1}{600})^{3}(1 - \frac{1}{600} )^{0} \Rightarrow (\frac{1}{600})^{3} \approx 4.6\times10^{-9}](https://tex.z-dn.net/?f=P%28Y_i%3D3%29%20%3D%20%7B3%20%5Cchoose%203%7D%28%5Cfrac%7B1%7D%7B600%7D%29%5E%7B3%7D%281%20-%20%5Cfrac%7B1%7D%7B600%7D%20%29%5E%7B0%7D%20%5CRightarrow%20%28%5Cfrac%7B1%7D%7B600%7D%29%5E%7B3%7D%20%5Capprox%204.6%5Ctimes10%5E%7B-9%7D)
But this holds for only one of the three groups and need to compute for all possible outcomes. Since the condition is that the three friends stay together, there are three possibilities: They are assign to the first group or the second group or the third group. We are not interested in one of them being assigned to another group. We want:
![P(Y_1 = 3 \cup Y_2 = 3 \cup Y_3 = 3) = P(Y_1 = 3) + P(Y_2 = 3) + P(Y_3 = 3)\\ P(Y_1 = 3 \cup Y_2 = 3 \cup Y_3 = 3) = 4.6\times10^{-9} + 4.6\times10^{-9} + 4.6\times10^{-9} = 1.4\times10^{-8}](https://tex.z-dn.net/?f=P%28Y_1%20%3D%203%20%5Ccup%20Y_2%20%3D%203%20%5Ccup%20Y_3%20%3D%203%29%20%3D%20P%28Y_1%20%3D%203%29%20%2B%20P%28Y_2%20%3D%203%29%20%2B%20P%28Y_3%20%3D%203%29%5C%5C%20P%28Y_1%20%3D%203%20%5Ccup%20Y_2%20%3D%203%20%5Ccup%20Y_3%20%3D%203%29%20%3D%204.6%5Ctimes10%5E%7B-9%7D%20%2B%204.6%5Ctimes10%5E%7B-9%7D%20%2B%204.6%5Ctimes10%5E%7B-9%7D%20%3D%201.4%5Ctimes10%5E%7B-8%7D)
Which is very close to zero.