What is the probability that all the aces will appear

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The discussion focuses on calculating probabilities in various scenarios involving card decks and dice rolls. It specifically addresses the probability that all aces appear before any tens in a shuffled deck of cards, the likelihood of rolling at least one six in four rolls of a fair die compared to achieving a sum of 12 in 24 rolls of a pair of dice, and the probability of a student answering at least half of the questions correctly on a true/false test while guessing. The calculations involve combinatorial probability and the binomial distribution.

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1) a deck of cards is shuffled and the cards turned up one at a time. What is the probability that all the aces will appear before any of the tens?

2) which is more likely-- at least one 6 in 4 rolls of a fair die or at least one sum of 12 in 24 rolls of a pair of dice?

3) a true false test has 4 questions. the student is guessing.
a) What is the probability the student answers at least half of the questions correctly?
b) now, the student knows the answer of question2 (false). WHat is the probability that the student answers at least half of the questions correctly
 
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hi hmcc, what have you tried?
 

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