PigeonHole principle
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PigeonHole principle
1. A box contains 6 red balls, 8 green balls, 10 blue balls, 12 yellow balls, and 15 white balls. What is the bare minimum of balls we must select at random from the box to ensure that we get 9 balls of the same color?
1.1. How many people in a group of 100 have the same birthday month?
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- A bag contains 8 black, 7 yellow, and 10 green marbles. If a sample of 6 is drawn at random, how many samples are possible in which the marbles are: a. all green? b. 2 black, 2 yellow, and 2 green?A. A pair of dice is rolled. If X is the sum of pairs of numbers. 1. What is the P(X) which is divisible by 4? 2. What is P(X) which is divisible by 3?10 In how many ways can one to put seven different colored balls into six identical boxes, if some boxes can remain empty ? 121; (2) 470; (3) 140; 4301; 5235; 6 63; 876; 8 350.
- 11. In the Colorado Power Ball Lottery you choose 5 white numbered balls from a group of 75 and 1 red ball from a group of 15. How many possible winning combinations are there? How many winning combinations contain the white number 2 and 8? 3 of 34. A player spins a fair spinner with 3 sections, numbered 0, 2, and 6. Then the player tosses a fair die with four faces, numbered 1, 2, 3, and 4. The player's score is determined by doubling the number on the die, and then subtracting the number on the spinner. What is the average score for this game?14 16 18 a) How many times were the sum of the three dice more than 14? b) What proportion of the time was the sum of the three dice more than 14? c) How many times were the sum of the three dice at most 7? d) What proportion of the time was the sum of the three dice at most 7? Question Help: D Post to forum 00000 0000 00000000000 000000002 0000000000000 0000000f 000000 00000ot 00 0000000 0000to 0000 OF 00
- 8. You blindfold your friend. You give him a bowl that contains seven green balls and five yellow balls. What is the minimum number of balls your friend needs to pick to be sure that they pick out all five yellow balls? (The balls are selected without replacement - once a ball is chosen it is not put back into the bowl).7.discrete math
- 23. The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.Construct a 92% Confidence Interval for the true proportion of girls in the ages 8 to 12 beginning ice-skating classes at the Ice Chalet.Calculate the following. (Round your answers to two decimal places.) (a) lower limit________________(b) upper limit_______________(c) error bound _______________A card game contains 52 cards where 13 are of hearts, 13 are spades, 13 are clubs and 13 are diamonds. What is the minimum amount of cards that we would need to pull to get at least 6 cards of the same symbol?discrete math