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By Yasui Y.

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A spaceship with a cross-surface of 100 square feet is to be placed in orbit at this altitude. 01K , K = 0, 1, 2, . . What is the probability that the vehicle will be destroyed by meteoric particles during a one-day mission? 14. Prove that if An is a sequence of sets in the algebra A such that An+1 ⊂ An and ∩∞ n=1 An = ∅, then if P is a probability measure on A, lim n→∞ P (An ) = 0. 15. Show that if B ⊂ A, P (B |A ) ≥ P (B). 16. Show that if A ⊂ B, P (B |A ) = 1. 17. Show that P (B ∪ C |A ) = P (B |A ) + P (C |A ) if B ∩ C = ∅.

2:1 Redundancy. 7. 4:3 Redundancy. 6. 8. Probability of Failure. 7. A register contains 16 random binary digits which are mutually independent. Each digit is a 0 or 1 with equal probability. (a) Describe a probability space { , A, P } corresponding to the contents of the register. How many points does have? (b) Express each of the following four events explicitly as a subset of the probability of these events: i. ii. iii. iv. and find The register contains 1111001100110101. The register contains exactly 4 zeros.

The best five out of seven cards. In this game, you received an Ace and a Jack as your two hole cards, and your opponent received two Aces. Believing that you had a strong hand (you did not) you bet everything that you had in hopes of getting your opponent to fold his hand. However, your opponent, believing that he had a strong hand (he did), called your bet, and now you need the five community cards to keep you from going broke. The first four cards were a King, a 5, a Jack, and then a 2. There is only one more card to be dealt, and the only card that will save you is a Jack.

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