Vrijeme: 08:40
Markov lanac | Marko's chain #1
Marko ima magični tetraedar na čijim stranama pišu brojevi
,
,
i
. Ako je u nekom bacanju pao broj
, u idućem bacanju je vjerojatnost za svaki broj
. Ako je pao broj
, u idućem bacanju mogu pasti samo
ili
, oba s vjerojatnošću
. Marku je u prvom bacanju pao broj
i odlučuje bacati dok ne dobije
ili
. Kolika je vjerojatnost da će dobiti
?
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
![0.25](/media/m/d/e/8/de8ef6213c2a4b4eb206efa9d49f4d5e.png)
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)
![0.5](/media/m/3/6/6/366b9873659ceda31da6fe8f74f95f65.png)
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)
Marko has magic tetrahedron with numbers
,
,
and
written on its sides. If Marko throws
, then in the next throw, probability of getting any number is
. If he throws
, in the next throw he can only get
or
, each with probability of
. In the first throw, Marko got
, and he keeps throwing until he gets
or
. What is the probability that he will get
?
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
![0.25](/media/m/d/e/8/de8ef6213c2a4b4eb206efa9d49f4d5e.png)
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)
![0.5](/media/m/3/6/6/366b9873659ceda31da6fe8f74f95f65.png)
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)