Amy and Blake are each dealt two cards from a standard, 52-card deck. Amy's cards are known, Blake's cards are unknown. In which of these two scenarios is it MORE LIKELY that Blake has a pair:
A) Amy: Queen Queen Blake: face down, face down
B) Amy: Queen Five Blake: face down, face down
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B)Amy queen five and Blake face down face down because in option a there are 2 queen left in deck so probablity is 2/50 while in option B 3queens are left in deck so probablity is 3/50 and same about 5 so option B is more likely to happen.
In scenario A, Amy has been dealt two queens, so there are only two queens left in the deck that Blake can have as a pair. Therefore, in this scenario, the chances of Blake having a pair are relatively low.
In scenario B, Amy has been dealt a queen and a five, so there are still three queens left in the deck that Blake can have as a pair. Therefore, in this scenario, the chances of Blake having a pair are relatively higher compared to scenario A.
Thus, it is MORE LIKELY that Blake has a pair in scenario B (Amy: Queen Five, Blake: face down, face down).
To determine which scenario is more likely for Blake to have a pair, we need to consider the number of pairs that could potentially be formed in each scenario.
In scenario A, Amy has a pair of Queens. This means that there are already two Queens out of the remaining 50 unseen cards. For Blake to have a pair, his two face-down cards must match. There are three remaining Queens in the deck, so the probability of Blake having a pair is (3/50) * 1/49 = 3/2450.
In scenario B, Amy has a Queen and a Five. There is no pair among Amy's cards. For Blake to have a pair, his two face-down cards must match. There are four remaining Fives in the deck, so the probability of Blake having a pair is (4/50) * 1/49 = 4/2450.
Comparing the probabilities, we can see that scenario B has a higher likelihood for Blake to have a pair compared to scenario A. Therefore, in scenario B (Amy: Queen Five Blake: face down, face down), it is MORE LIKELY that Blake has a pair.