(a) If one student is selected at random from these 400 students, find the probability that this student Prefers sugar free drinks (i) (ii) Prefers juice (iii) Prefers regular juice
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- Kim and Susan are playing a tennis match where the winner must win 2 sets in order to win the match. For each set the probability that Kim wins is 0.59. The probability of Kim winning the set is not affected by who has won any previous sets. (a) What is the probability that Kim wins the match? (b) What is the probability that Kim wins the match in exactly 2 sets (i.e. only 2 sets are played and Kim is the one who ends up winning)? (c) What is the probability that 3 sets are played?A group of botanists is studying the distribution of carnations in a field. The field is divided into a number of equal sized squares. The mean number of carnations per square is assumed to be 3. The carnations are distributed randomly throughout the field. Find the probability that: (b) (i) there will be more than two carnations. (ii) either five or six carnations.An average of 1 package is sent to a server in 1 second. The server, on the other hand, prepares a document using the 5 packages received. The time between packets is modeled as an exponential random variable. Let X be a random variable expressing the time it takes the server to prepare a document. The time taken to prepare a document; a) Find the probability that it is more than 10 seconds.(with detail) b) Find the probability that it is between 5 seconds and 10 seconds. (with detail)
- The probability that a patient will be cured of corona virus when injected with the new vaccine is 0.8. FInd the probability taht exactly 3 out of the 8 corona virus patients will be cured on being injected with the vaccine.A group of 200 UTAR students were asked whether they played soccer or basketball. Among the group, 140 said they played soccer, 30 said they played basketball and 20 said they played both soccer and basketball. (i) Calculate the probability that a student selected at random from the group plays soccer given that he plays basketball. Calculate the probability that a student selected at random from the group plays basketball given that he plays soccer. (ii) (iii) Calculate the probability that a student selected at random from the group plays soccer given that he plays one sport only.Ezra buys a bag of cookies that contains 9 chocolate chip cookies, 7 peanut butter cookies, 4 sugar cookies and 4 oatmeal cookies.What is the probability that Ezra reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects a chocolate chip cookie? Give your answer as a fraction, or accurate to at least 4 decimal places.
- The mosquitos are out in your back yard, and they bite you at random times. Each bite happens independently of the last bite. The average time between bites is 2.501 minutes. What is the probability that it takes longer than 1 minutes for them to first bite you?Sneakers are no longer just for the young. In fact, most adults own multiple pairs of sneakers. Table gives the fraction of US adults 20 years of age and older who own five or more pairs of wearable sneakers, along with the fraction of the US adult population 20 years or older in each of five age groups. (1) Find the probability that the person owned at least five pairs of wearable sneakers. (2) Find the probability that the person selected was 65 years of age or older, given that the person owned at least five pairs of wearable sneakers. Groups and Ages G1 (20-24) G2 (25-34) G3 (35-49) G4 (50-64) G5 (≥65) Fraction with ≥ 5 pairs 0.26 0.2 0.13 0.18 0.14 Fraction of US Adult 20 and Older 0.09 0.18 0.3 0.25 0.18A coin is in one of 5 boxes. The probability that it is in the ith box is (i/15). If you search in the ith box and it is there, you find it with probability (4/5). Find the probability that the coin is in the 3rd box given that you have looked in the 1st box and did not find it.
- In a city, there are two independent firetrucks, the probability that the first firetruck access to the fire place during ten minutes is 0.75, while the probability that the second firetruck access the fire place during ten minutes is 0.6. what is the probability that both firetrucks can access the fire place at the same time?For any day in July, there is a 20% chance of rainfall. An engineering construction company plans to cast a slabthat requires no rainfall during its casting period extending over 5 days. What is the probability of having no rainfallduring the casting period and one rainy day during the casting period?