Statistical analysis of disappearing eagles 
Satellite tagged eagles are going missing in Scotland, and the table above shows the tag fate by tag model. I am particularly interested in those tags that are "Stopped - no malfunction", because it is possible that these birds are also being killed and the bodies and tags are being disposed of. 
I have seen it stated that this table and this table alone is evidence that "Even with the remotest statistical analysis it is clear that there are relationships between "Stopped - No Malfunction" and the type of tag used" So my question is, can this statement be backed up?
42/135  (31%) tags stopped for all types 
 8/17   (47%) tags stopped for 80NS     
29/77   (38%) tags stopped for 70GPS    
 3/22   (14%) tags stopped for 105GPS   
 2/13   (15%) tags stopped for 70GSM    
 0/6     (0%) tags stopped for 95BTOGSM 

So I guess that the statement is true if the 80NS failure rate of 47% is significantly worse than global average of 31%.  And it would not be true if the probability of getting 8 failures in a random sample of 17 tags out of the 135 was actually quite high. More abstractly, if there were 42 black balls and 93 white balls in a bag and I picked out 17 at random, what is the probability I'd pick 8 black ones and 9 white ones?
I can work out the probability of the first 8 being black as (42/135) * (41/134) etc. but I'm stuck trying to work out the likelihood of any 8 of the 17 being black

EDIT: The satellite tags were attached to birds over a 13 year period, 2004 to 2016. This table shows 131 tags rather than 135. 4 tags were excluded because they could not ascertain the precise deployment location of four early tags. 

Here is another table from the report that shows some data about the life of the 70GPS/70GSM tags:

 A: I found a way to get to my answer from this comment "look up the hypergeometric distribution" on math.stackexchange: 
From Wikipedia's entry on hypergeometric distribution

In probability theory and statistics, the hypergeometric distribution
  is a discrete probability distribution that describes the probability
  of k successes (random draws for which the object drawn has a
  specified feature) in n draws, without replacement.

Then, using an online Hypergeometric Calculator and the following figures:
Population: 135
Number of successes in population: 42
Sample size: 17
Number of successes in sample: 8
I find that the probability of getting exactly 8 is 0.0703, and the probability of getting 8 or more is 0.1095
I think the "8 or more" figure is the relevant one in this case, and I have to say that this probability is lower than my intuition predicted.
So the numbers suggest that there is an 89% probability that there is something different about the failure rate when segregated by tag type. That does not mean that the cause of the difference is the tag type. 
