Show all work in details for esch question. Po 4; Qs Q-5,- :s 3Q 5; Qs-4. EC-1 p

Question

Show all work in details for esch question. Po 4; Qs Q-5,- :s 3Q 5; Qs-4. EC-1 point each. 1. A box contains 5 colns with a Head on each side 8 eoims with a Tail on each side, and 3 fair coins. If one of these 16 colns is selected at randoen and tossed once, what is the probability that a Hend will be obtained? 2. If five letters are placed at random in five envwelopes, what is the probability that exactly one letter will be placed in the cortect envelope. 3. If the e letters a,ce.llsu,u are arranuged in a random order, what is the proba bility that they will spell the word "caleculus"? 4. Prove that for all positive integers n and k (n 2 k) 5. An elevator in a building starts with 5 pasengers and stops at seven Bloons every passenger is equally likely to get off at enchs floor and all the assen- gers leave independently of each other, what is the probability that no two passengers will get off at the same floor? 6. For two arbitrary events A and B prove that Extra Credit 7. For auy three events A, B and Dsuch that P(D)0 prove that 8. Prove that Hint: Use the Binomial Theorem.]

Explanation / Answer

2) five letters are placed at random in five evenvelops

and we find out the probability that one letters are placed in correct envelop

sample space=

n(s)=5!

event=

n(E)=5c1=5

probability =

p(E)=1/24

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