-Given that P(a) = 0.2 and P(b) = 0.6, in which of the following joint probability table: are P(A) and P(B) absolutely independent? b -b A) a 0.16 0.04 -a 0.42 0.28 B) b -b a 0.10 0.10 -a 0.50 0.30
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- A group of 20 students have been on holiday abroad and are returning to Norway. In the group, there are 7 who have bought too much alcohol on duty-free and none of them informs the customs officers about it. Customs officers randomly select 5 people from these 20 students for control. We let the variable X be the number of students among the 5 selected who have bought too much alcohol. (a) What type of probability distribution does the variable X have? Write down the formula for the point probabilities. (b) What is the probability that none of those checked has bought too much? (c) What is the probability that at least 3 of the 5 controlled students have bought too much?Find the missing probability. 7) P(A) = 0.4 P(A and B) = 0.18 P(BA) = ? 9) P(A and B) = 0.035 P(BA)=0.05 P(A) = ? 11) P(B) = 0.5 P(A/B) = 0.54 P(A and B) = ? 13) P(A)=0.35 P(A and B)= 0.14 P(B|A) = ? 8) P(A and B) = 0.1 P(BA)=0.25 P(A) = ? 10) P(A)=0.6 P(BA) = 0.55 P(A and B) = ? 12) P(B) = 0.25 P(A and B)=0.07 P(A/B) = ? 14) P(A and B) = 0.08 P(BA)=0.4 P(4)= ? -1-You are given four events A, B, C, D that are independent, and whose probabilities are Pr(A) = 0.6, Pr(B) = 0.5, Pr(C) = 0.4, and Pr(D) = 0.3. Find the probability that at least two events of these events happen. O 0.2908 O 0.4684 O 0.3748 O 0.7092 O 0.6140
- You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest centIf the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the probability that the box will contain less than the advertised weight of 453 g? (Round your answer to 4 decimal places.) Probability:???????????The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17, respectively. Find the probability that in this 30-minute period (a) more than 2 cars receive gas; (b) at most 4 cars receive gas; (C) 4 or more cars receive gas
- On cloudy days, Lucy has ramen for lunch with probability 0.4.On non-cloudy days, she has ramen with probability 0.2.There's a probability of 0.3 that it'll be cloudy tomorrow.What's the probability that she eats ramen tomorrow?Q13: If A and B are two events such that P(A) = p₁, P(B) = P2, P(ANB) = P3, then the probability that A occurs but B does not occur is: (a) P1 - P3 (b) P1 P2 (c) P1 - P2P3 (d) P1 — P1P2Let A and B be mutually exclusive events, such that P(A) = 0.2371 and P(B) = 0.1133. Find the following probabilities: P(A and B)= P(A or B)= % (Round the answer to 2 decimals) % (Round the answer to 2 decimals)
- 3. For two independent events, A and B, P(A)=D0.1 and P(B)-D0.5. Enter your probabilities as decimals. 3(a) P(A and B) = 3(b) P(A| B) = %3! 3(c) P(A or B) =When sent a questionnaire, 50% of the recipients respond immediately. Of those who do not respond immediately, 60% respond when sent a follow-up letter. If the questionnaire is sent to 4 persons and a follow-up letter is sent to any of the 4 who do not respond immediately, what is the probability that at least 3 never respond? A D E (0.2) 4 + 4.(0.2) ³. (0.8) (0.2)4 + 4.(0.2).(0.8)³ (0.4) 4 + 4C (0.4) ³. (0.6) (0.9)4 + 4.(0.9) ³. (0.1) 4.(0.2) ³ (0.8)Given two events A and B, if P(A) = 0.4 and P(B) = 0.6, calculate the conditional probability P(A|B) if they are disjoint.