1- The probability that Mohamed passes Mathematics is 0.5, and the probability that Mohamed and Omar pass is 0.25. What is the probability that Omar passes given that Mohamed passes?
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- Suppose that your friend Kamala randomly chooses a number between 1 and 13 (including both 1 and 13) and asks you to guess what it is. Answer the following questions: 1. What is the probability she is thinking of an even number? 2. What is the probability the number she is thinking of has a 1 in it? 3. What is the probability that the number she is thinking of is at least 5?A hacker is trying to guess someone's password.The hacker knows that the password is 4 digits long,and that each digit could be a number between 0 and 3.Assume that the hacker makes random guesses.What is the probability that the hacker guesses the password right on her first try?If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365, 364/365. Explain why this is so. (Ignore leap years and assume 365 days in a year.)
- Suppose that it is equally likely for a child to be a boy or a girl. Suppose a parent tells you that she or he has 6 children. What is the probability that at least one is a boy given that at least 5 of the children are girls?A certain tennis player makes a successful first serve 78% of the time. Assume that each serve is independent of the others. If she serves 9times, what's the probability she gets: Part 1 a) The probability that she gets all 9 serves in is _______________ (Round to three decimal places as needed.). Part 2 b) The probability she gets exactly 4 serves in is _______________ (Round to three decimal places as needed.) Part 3 c) The probability she gets at least 7 serves in is ______________________ (Round to three decimal places as needed.) Part 4 d) The probability that there are no more than 6 serves in is __________ (Round to three decimal places as needed.)21. A company in New Jersey is hiring 8 people for a position. Of the applicants, 10 are from New Jersey, 8 are from New York, and 7 are from Pennsylvania. What is the probability that of the 8 people hired, exactly 2 are from New Jersey, and what is the probability at least two are from New Jersey? Round off to 3 decimal places. _________ and ________
- Suppose that ina certain small town it either rains or is sunny every day. A meteorologist notes that when it is sunny in this town, it will be sunny the next day with probability 0.6. If it rains, it will be sunny the next day with probability 0.7. Answer the following questions: 1. What is the probability that it will rain the next day if it was sunny the previous day?1. Considering the days when Ali has classes, the probability that he falls sick is that he is absent from classes is 30 The probability The probability that he is sick or absent from classes is 15 (a) What is the probability that he is sick and absent from classes? (b) What is the probability that he is not sick but absent from classes?Mustafiz has 95 balls which are labeled with the numbers from 1 to 95. He draws out a ball from the bag, records down the number and then puts it back in the bag. He does this a total of 3 times (hence has 3 numbers). Now answer the following questions. i. What is the probability that all the numbers are different? [Give your answer upto 4 decimal places] ii. What is the probability that at least 2 of the numbers are equal? (Give your answer upto 4 decimal places)
- Binary digits, that is 0 and 1 are sent down a noisy communications channel. They are received as sent with probability 0.9 but errors occur with probability 0.1. To improve the reliability of the channel we repeat each digit in the message three times. (a) Let A=”101 was received” and B=”111 was sent”. What is the probability that 111 was sent given that we received 101?, i.e., What is P(B|A)? (b) Let A=”000 was received” and B=”111 was sent”. What is the probability that 111 was sent given that we received 000?i.e., What is P(B|A)?But change the problem as follows: The probability that each link is working is 0.95. Also, if the message was transmitted successfully, what is the probability that the middle link was working? (Hint: Messages get sent through all three paths. At least one of the three paths must be successful in order for B to receive the message.)
