Question

There are two decks of cards. Deck 1 contains 50 Red cards, 30 Blue cards, and 20 Jokers. Deck 2 contains 10, 80, 10, respectively. At each stage, we select a card from a deck. If we select a Red card then, we select a card of the other deck at the next stage. If we select a Blue card then, we select a card from the same deck at the next stage. If at any stage, a Joker is selected, then the game ends. Cards are always replaced in the decks. Set up a Markov chain by defining your states properly.

Answer #1

Given that Two deck cards

Deck 1 Contains Red 50

Blue 30

Jocker 20

Total=50+30+20=100

Probability of selecting red card=

Probability of selecting blue card=

Probability of selecting jocker cards=

In Deck2 Contains Red 10

Blue 80

Jocker 10

Total=10+80+10=100

Probability of selecting red card=

Probability of selecting blue card=

Probability of selecting jocker card=

Here there are three stage

Stage 1: Selecting the from deck

Stage 2: Selecting the card other deck

Stage3: Game end

The transition matrix is

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