# Bernoulli distribution/ SOME probability/conjugate prior

I would like to know what "SOME probability of seeing tail" means in the second answer here. I.e. how much is it?

EDIT: I do not understand how can I see that there is SOME probability of seeing Tail just from the shape of the 4th picture. Can someone elaborate on this? May the word "SOME" be made precise in the sense of magnitude of that quantity?

• "Some" means greater then zero. What is unclear for you? – Tim Dec 25 '18 at 17:37
• Thank you for your reply. What I do not understand is how to read "SOME" from the 4th picture. – user2925716 Dec 25 '18 at 17:38
• What do you mean by "how to read"? You mean English pronunciation? – Tim Dec 25 '18 at 17:39
• No :-) How do I understand or read off from the 4th picture that there is SOME probability of seeing Tail. It is somehow because that it is curved towards the 0 at the r.h.s.? – user2925716 Dec 25 '18 at 17:41
• @Tim I did my best, please see EDIT. – user2925716 Dec 25 '18 at 18:04

I would try running the commands below:

print(dbeta(seq(0,1,0.01),3,2))
plot(dbeta(seq(0,1,0.01),3,2),type='l')


the plot should be the same as the one in the link (see below for reference).

the print statement prints the probabilities of the dbeta:  [1] 0.000000 0.001188 0.004704 0.010476 0.018432 0.028500 0.040608 0.054684 [9] 0.070656 0.088452 0.108000 0.129228 0.152064 0.176436 0.202272 0.229500 [17] 0.258048 0.287844 0.318816 0.350892 0.384000 0.418068 0.453024 0.488796 [25] 0.525312 0.562500 0.600288 0.638604 0.677376 0.716532 0.756000 0.795708 [33] 0.835584 0.875556 0.915552 0.955500 0.995328 1.034964 1.074336 1.113372 [41] 1.152000 1.190148 1.227744 1.264716 1.300992 1.336500 1.371168 1.404924 [49] 1.437696 1.469412 1.500000 1.529388 1.557504 1.584276 1.609632 1.633500 [57] 1.655808 1.676484 1.695456 1.712652 1.728000 1.741428 1.752864 1.762236 [65] 1.769472 1.774500 1.777248 1.777644 1.775616 1.771092 1.764000 1.754268 [73] 1.741824 1.726596 1.708512 1.687500 1.663488 1.636404 1.606176 1.572732 [81] 1.536000 1.495908 1.452384 1.405356 1.354752 1.300500 1.242528 1.180764 [89] 1.115136 1.045572 0.972000 0.894348 0.812544 0.726516 0.636192 0.541500 [97] 0.442368 0.338724 0.230496 0.117612 0.000000  The value at p=1 with index 100 is 0.0 which means that there is some probability that you will see a tail. This can be inferred from the sharp dip of the curve.

When the toss was heads, the probability at 1 kept going up, indicating a completely head biased coin, but as soon as you saw the tail the probability at 1 went down showing that it not completely head biased, because a tail was observed.

It might be interesting to observe that the value at p=0 is also zero, meaning that the coin is neither completely head nor completely tail biased.

Hope this helps.