+0 A standard deck of cards contains 52 cards. These 52 cards are arranged in a circle, at random. Find the expected number of pairs of adjacent cards that are both Aces.
0 2. When the set of natural numbers is listed in ascending order, what is the smallest prime number that occurs after a sequence of five consecutive positive integers all of which are non prime?
+129850 2. When the set of natural numbers is listed in ascending order, what is the smallest prime number that occurs after a sequence of five consecutive positive integers all of which are non prime?
24,25,26,27,28
Smallest prime = 29
+297 I'll try my best on this one, I'm not particularly good with this topic.
So the first Ace can appear anywhere, so 52 choices, times 4 since it could be any of the 4 aces.
The ace adjacent to it has 2 choices, left or right, and has 3 choices on which type of ace.
The probability of this happening is \(\frac{52\cdot4\cdot2\cdot3}{52\cdot52\cdot2\cdot51}\) which will end up being \(\frac{1}{221}\)
so the expected number of times is 0.
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