Introductory Probability HW 1) A professional magician claims to be able to read

Question

Introductory Probability HW 1) A professional magician claims to be able to read minds. In experiment is conducted with 5 cards numbered 1 to 5. A person order to test his claims, an concentrates on the numbers of two of the cards, and the magician attempts to read his mind and name the two cards. What is the probability that he wil correctily name the two cards, on the assumption that he is merely guessing? 2) If you roll a regular 6-sided die twice, what is the probability of getting a sum of 5? 3) If you choose a random integer between 21 and 40, inclusive, what is the probability that it is prime? 4) Given a regular 52-card deck, what is the probability of drawing a black card and then a red card, without replacement? 5) Given 3 regular 6-sided dice, what is the probability of rolling a sum of 10 6) Given a regular 52-card deck, what is the probability of getting a 5-card hand that consists of all cards from the same suit? In the California lottery, to play, all you have to do is pick five numbers from 1 to 47 and one MEGA number from 1 to 27. 7) To win first prize, you must match all 6 numbers. What is the probability of winning first prize? o win second prize, you must match any 5 of the 6 winning numbers. What is the probability of winning second prize? 8) T 9) To win third prize, you must match any four of the six winning numbers. What is the probability of winning third prize? has two drawers. Box A contains a gold 10) Each of three boxes, identical in appearance coin i n each drawer, Box B contains a silver coin in each drawer, and Box C contains a gold coin in drawer 1 and a silver coin in the other. A box is chosen, one of its drawers is opened and a silver coin is found. What is the probability that the other drawer contains a gold coin?

Explanation / Answer

1) the number of ways 2 card can be named = 5C2 = 10

there is only of them which is correct

hence required probability = 1/10=0.1

2)P(X+Y =5) = 4/36=1/9   {(1,4),(2,3)<(3,2)<(4,1)}

3)prime number between 21 and 40 = 23,29,31,37

hence required probability = 4 /20 = 0.2

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