Question

I bought a dozen eggs. the weights in grams are as follow: 54,55,57,59,59,61,63,66,66,67,67,77 grams. what is the probability I randomly pick 2 eggs that weight over 133 grams?

Answer 1

None of the 12 eggs weigh over 133 grams. Therefore the probability of randomly picking 2 eggs that weigh over 133 grams is zero.
Have you typed the question correctly?

Answer 2

sorry i ment randomly picking two, that added together, weight >133g

Answer 3

so like 77+67 would be 144g

Answer 4

well you need to find the number of possible 2 egg choices

12 x 11 =

than the number where the combined weight > 133

the P( combined weight > 133) = number of combined > 133
------------------------
total number of arrangements

Answer 5

The order in the selection of each pair of eggs does not affect the combined weight of the 2 eggs. Therefore the number of combinations of the 12 eggs taken 2 at a time is
\[12C2=\frac{12!}{2!10!}=\frac{12\times 11}{2}\]

Answer 6

i agree with that. Im having trouble coming up with a clear way of thinking about the >133 part

Answer 7

like if 77 then 9 choices
if 67 then 4 choices (66,66,67,77)
if 66 then 3 choices(67,67,77)

Answer 8

16/66? im afraid im overcounting some of them

Answer 9

yep thats the way to look at it

Answer 10

no thats wrong because i counted 77 twice

Answer 11

i think anyway

Answer 12

My take on combinations weighing more than 133 grams:
Egg weight Combinations
54 0
55 0
57 1
59 1
59 1
61 1
63 1
66 1
66 1
67 1
67 1
67 + 67 1

Answer 13

@sahsah The question states that the combined weight of the 2 eggs is over 133 grams (not equal to 133 grams).