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Probability - Estimation of certainty based on random samples

Question 1.

We have 4 decks of cards, and each deck is missing a different suit:

1.            D(R), S(B), C(B)

2. H(R),            S(B), C(B)

3. H(R), D(R),          C(B)

4. H(R), D(R), S(B)

H(R) represents Hearts(Red). There are 39 (3x13) cards in each deck.

We pick one deck at random,  then we draw two cards at random from that deck.

On turning over the two cards, we see that they are both Red (Hearts or Diamonds).

Which deck did we pick (1,2,3 or 4), and how certain are you of that?

Question 2.

We have two weighted coins.

One coin (H) has a 2/3 chance of landing heads-up.

The other coin (T) has a 2/3 chance of landing tails-up.

We pick one of these coins at random, leaving the other coin aside.

(a) On the first toss it lands heads-up. What is the probability that it is coin H.

(b) On the second toss it also lands heads-up. What is the probability that it is coin H.

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Replies to This Discussion

It has been a while since I've done probability and statistics, but, for the second problem, a tree can be made to find the probability

Toss
CoinH CoinT //each coin has an equal probability of being chosen
HHT TTH //heads and tails still have an equal probability

On the first toss the probability the coin is H is 1/3. (1/2 from coin H and 2/3 heads from coin H)
Since the second probability is the same, multiply 1/3 by 1/3 to get 1/9.

Although I'm not 100% certain