Muk Man said:actually..."if you have 6 prizes
flip 2
if the 2 you flip are not the card you need. you now have a 25% (1/4) cahnce of getting the prize you need
with out hermit you only have a 16% (1/6).
They way i look at it, is that you have a 58% chance of getting the prize you need with hermit.
First you have a 33% chance that you will flip it over with hermit (2/6=1/3), if you dont you now have a 25%(1/4) chance of drawing it that gives you 2 seperate chances...33+25= 58% chance of getting the card you want /need (+/- your luck factor)
And thats only 1 hermit.....now add a second. or what if you ko an ex...???
"Men lie, women lie, but numbers dont lie" Jay Z
Ehhhhh... No oO
Ok lets name the "events" (I dont know the correct mathematical term because English is not my native language. In German, its "Ereignis", I hope "event" is understood.)
A=You flip over the card you need by using Hermit
B=You draw the card you need as your prize.
Ok, P(A) is obviously 33,3 % as you pointed out. But what we want is P(B). P(B AND A) is
P(A) times P(B under the condition A) due to the defintion of conditional probability.
P(B under the condition A) is obviously 100%. If A happens, you flipped over the right card, so you will draw it with your next prize (if you're not stupid :wink: ). So P(B AND A) is
33% times 100% = 33%
Next we need is P(B and (NOT A)).
Thats again using the definiton of conditional probability
P(NOT A) times P(B under the condition (NOT A))
P(B under the condition (NOT A)) is, as you stated, 25%. One of 4 cards.
P(NOT A) is 1- P(A) = 66,6%
So, P(B and (NOT A)) is 25% times 66,6%= 16,6%
Next step is to use one of the axioms of Kolmogoroff:
When two events A and B are disjoint, P(A OR B) is P(A) + P(B)
P(( B AND (NOT A)) OR (B AND A)) is P(B AND (A OR (NOT A)) is P(B AND OMEGA) is P(B)
So, P(B) is 33%+16,6% is 50% (not only approximately, I rounded the percent numbers, 50 % is exact).
Not 58 %.
I've done this detailed... Hope it helps...