Jaxon remembers that the passcode contains the digits 1, 2, 3 and 4, but he cannot recall their order. If Jaxon randomly enters these four digits, what is the chance that he will enter the correct code?
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- Each of the numbers 0 - 9 is written on a different golf ball. The ten golf balls are put in a paper bag. If two of these golf balls are selected from the bag, without replacement, find the probability that both numbers are less than 4.A popular gambling game called keno, first introduced in China over 2000 years ago, is played in many casinos. In keno, there are 80 balls numbered from 1 to 80. The casino randomly chooses 20 balls from the 80 balls. These are "lucky balls" because if a gambler chooses some of the numbers on these balls, there is a possibility of winning money. The amount that is won depends on the number of lucky numbers the gambler has selected. The number of ways in which a casino can choose 20 balls from 80 is C(80, 20) = 80! 20! · 60! ≈ 3,535,000,000,000,000,000. Once the casino chooses the 20 lucky balls, the remaining 60 balls are unlucky for the gambler. A gambler who chooses 5 numbers will have from 0 to 5 lucky numbers.Let's consider the case in which 2 of the 5 numbers chosen by the gambler are lucky numbers. Because 5 numbers were chosen, there must be 3 unlucky numbers among the 5 numbers. The number of ways of choosing 2 lucky numbers from 20 lucky numbers is C(20, 2). The…A group of six friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over. The designated cards are: 9 of Hearts, Jack of Diamonds. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over. In how many ways can you deal the cards WITHOUT getting one of the designated cards? (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.) In how many ways…
- A drunken man who has n keys wants to open the door if his office. He tries the keys at random, one by one, and the unsuccessful keys are eliminated. Show that at all times, no matter how many unsuccessful keys he has eliminated, the probability of finally locating the correct key is 1/nBenny is a messy student who keeps all his colored socks in a box. The box contains a total of 4 blue and 2 yellow socks. On the first day, while running late for class, he randomly selects (without replacement) two socks out of the box to wear. Assume the socks are indistinguishable from one another apart from color. The next day, Benny selects his socks again, but this time you are told that the first sock he has picked from the box is blue. What can you say about the probability he will end up wearing a matching pair of socks to class, in comparison to the first day? The probability of him wearing matching socks is higher than that of the first day The probability of him wearing matching socks is unchanged The probability of him wearing matching socks is lower than that of the first dayProfessor Adams wrote a book called Improving Your Memory. The professor claims that if you follow the program outlined in the book, your memory will definitely improve. Fifteen people took the professor's course, in which the book and its program were used. On the first day of class, everyone took a memory exam; and on the last day, everyone took a similar exam. The paired scores for each person follow. Last exam 223 122 117 274 89 77 112 207 91 132 173 113 217 289 71 First exam 171 116 116 209 66 87 168 199 77 111 143 19 196 242 91 Use a 0.01 level of significance to test the null hypothesis that the scores are the same whether or not people have taken the course against the alternate hypothesis that the scores of people who have taken the course are higher. 1.) Find the sample test statistic. (Use 2 decimal places for the value of x in your calculations. Use 2 decimal places for your answer.)2.) For the sign test, rank-sum test, and Spearman correlation coefficient test,…
- A researcher wants to determine if students retain more information when they learn in a classroom painted with bright colors than in a classroom painted with plain colors. The students are given the task of memorizing a list of 20 words in 5 minutes and are to write down as many words as they can remember 30 minutes later. The researcher conducts the experiment on students age 8 and 9 years. He assigns all of the students age 8 to the brightly colored room and all of the students age 9 to the plain colored room. Does this experimenter properly incorporate blocking into his design? O Yes. By blocking by room color, the researcher will be able to determine if students age 9 can retain more words than students age 8 can. O Yes. By having all of the students age 8 learn the words in the brightly colored room and the students age 9 in the plain colored room, he will increase the variability in the response variable (number of words recalled). O No. By assigning all of the students age 8 to…with work shownA new medical test is designed to quickly detect whether someone is infected by SARS or not. The test result could be either positive or negative. A group of1250 persons have gone through the test among which 1175 are free of SARS infection. Among the 1175 healthy people, 1170 of them return negative test results; while among the remaining infected people, 73 of them return positive test results.Based on the above information, if positive test result is returned for another person, is he/she infected by SARS or not?
- help meCertain app allows you to order from different types of cuisine. According with the app's records 23% of the orders are to an American food restaurant, 38% to an Asian food restaurant, 17% to a Mexican food restaurant, 6% to a Dessert place, and the rest are to other types of restaurants. Assume that incoming orders are independent of each other.Professor takes a random sample of students enrolled in Statistics 101 at Earth University where students are in one of four terms of their degrees.He finds the following: there are 25 first term students in the sample, 32 second term students, 18 third term students and 20 final term students. Professor decides to help you and use the R program to carry out this test. The code and output are as follows: null.probs = c(0.3,0.25,0.25,0.2)freqs = c(25, 32, 18, 20)chisq.test(freqs, p=null.probs)barplot(freqs, main="Distribution of Stat 101 Students", horiz=FALSE, xlab="Term", names.arg= c("First", "Second", "Third", "Fourth"), col="blue")Chi-squared test for given probabilities data: freqsX-squared = 4.830303, df = 3, p-value = 0.184653 Use the output to test the appropriate hypothesis. 1) Under the null hypothesis, how many students were expected to be enrolled in Term 1?(2 dp) 2) What are the degrees of freedom for this test? 3) Using a significance level of 0.05, would you (cHOOSE…