Problem 1. A coin with probability p of heads is tossed n times. Let E be the event "a head is obtained on the first toss" and Fk the event "exactly k heads are obtained". For which pairs of integers (n, k) are E and F independent?

Q: Two numbers are drawn successively at random with replacement from the set {0, 1, 2, 3, 4, 5, 6, 7,…

A: s : {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. select with replacement E : two numbers are same P(E) = ?

Q: Suppose you have three bowls, XX, YY, and ZZ, each with four balls with XX having 3 red and 1 blue,…

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Q: when a single die is rolled twice, let A be the event the die comes up ODD on the first roll and let…

A: When a single die is rolled twice, the all possible outcomes are: (1,1) (1,2) (1,3) (1,4) (1,5)…

Q: A hat contains 29 Orange slips of paper and 63 Green slips of paper (and nothing else). Two slips…

A: Total number of slips is 29+63 =92. It is known that hat contains 29 orange and 63 green slips. The…

Q: How can I solve this... Thank you for your help!

A: Given: Box A: 4 Red, 6 Blue Box B: 5 Red, 2 Blue Box C: 2 Red, 3 Blue Part a) P(All three balls are…

Q: Suppose you roll 6 ’fair’ dice (each has six sides numbered 1 to 6 and each side has an equal 1/6…

A: Given the experiment of rolling 6 fair dice and the events A, B and C are denotes Event A : exactly…

Q: A combination for a safe consists of four numbers between 0 and 9, and the safe is designed so that…

A: A combination of safe consists of four numbers between 0 and 9, the numbers can be repeated. Since…

Q: A standard six-sided die shows a number,1,2,3,4,5 or 6 on each of its sides. You roll the die once.…

A: From the given information, one dice is rolled and the dice shows the numbers 1, 2, 3, 4, 5 and 6.…

Q: Suppose a die is rolled twice and let A = {first toss is a prime} B = {first toss is a 2} Find the…

A: we have to find given probability.

Q: . An urn contains 5 red balls, 9 blue balls and 6 green balls. Use this information for both (a) and…

A: Urn contain 5 red, 9 blue, 6 green

Q: 5. Prove or disprove: If we roll 2d6 then the event that the first die is even is independent from…

A: To prove or disprove the statement, we need to show that the probability of the sum being 11 is the…

Q: 3.) If the probability of an event occurs is 0.7, determine the probability that the event does not…

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Q: Suppose that a certain precinct contains 12 voters, of which 7 are Democrats and 5 are Republicans.…

A: From the given information, there are 7 Democrats and 5 are Republicans. The total number of voters…

Q: If n people are present in a room. How large n need to be so that the probability of no two of them…

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Q: QUESTION 10 addition rule cats and dogs Among a group of 500 pet owners who visit the same pet…

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Q: 2. The letters of a string "MISSISSIPI" are arranged randomly in a line. If the event A represents…

A: Let's start by analyzing the given string "MISSISSIPI" and the events A and B.String: MISSISSIPI…

Q: QUESTION 19 Assuming that the population is half male and half female, what is the probability that…

A: Since you have posted multiple questions , we will solve first question  for you. To get the…

Q: What  is the probability that a hand of 5 cards chosen at random from a standard deck of 52 cards…

A: The 5 cards chosen need to have an odd number of cards from each of the four suits. There are 4…

Q: 13.) Suppose we throw 2 dice. Given that the sum of the dice is 10, what is the probability that one…

A: S={ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)  (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)  (3,1) (3,2) (3,3)…

Q: Problem (6): In a group of 30 students, 17 plays computer games, 10 play board games and 9 play…

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