- Let a coin and a die be tossed; let the sample space S consists of the twelve elements: S-(HI, H2, НЗ, Н4, Н5, Н6, Т1, Т2, ТЗ, Т4, Т5, Т6; (i) Express explicitly the following events: A={heads and an even number appear} B={a prime number appears} C={tails and an odd number appear} (ii) Express explicitly the event that: (a A or B occurs (b) B and C_OCCHIS
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- Ex.1 (on Probability handout) An electronic shop receives a box of 100 electronic devices of which 10 devices have type A defect, 8 devices have type B defect and 3 devices have both type A and B defects. If a device is picked at random from the box (so that each one of the 100 devices has an equal chance of being picked), find a) the sample space for the experiment b) the probability that the device picked has a type A defect c) the probability that the device picked has a type B defect d) the probability that the device picked has both types of defects e) the probability that the device picked has a defect f) the probability that the device picked is free of defectsConsider a die with only four sides, marked one, two, three, and four. (a) Write out a sample space for rolling a pair of these dice. Die Two 1 2 3 1, 1) (回v,回v)(回v国)(回レ回。 1 2. 2 Die One (3.2) (1 - , 1 - ) (4 v 2- ) (1- 3 - ) (4- , 4 -) 3 4 Assuming equally likely outcomes, find the probability that the sum of the dice is the given number. (Enter the probabilities as fractions.) (b) P(two) 1/240 X P(three) 1/60 X (c) P(four) 3/16 (d) (e) P(five) 1/15 X P(six) (f) 1/60 X (g) P(seven) 3/80 XQ4i) Hospitals records indicated that cardiac patients stayed in the intensive care unit of the hospital for the following number of days. Number of days stayed Frequency 4 32 5 18 6 25 7 19 3 10 Find the probabilities : a) A patient stayed exactly 7 days b) A patient stayed almost 6 days c) A patient stayed at least 5 days Q4.ii) a) Write the sample space if three (3) coins are tossed at a time. b) Find the probability of having at least 1 tail.
- 1- Let a coin and a die be tossed; let the sample space S consists of the twelve elements: S-{HI, H2, HЗ, Н4, H5, Н6, Т1, Т2, ТЗ, Т4, T5, Т6; (i) Express explicitly the following events: A={heads and an even number appear} B={a prime number appears} C={tails and an odd number appear} (ii) Express explicitly the event that: (а) А or B oссurs A or B Select one: О а. (Н2,НЗ,H5.T2,Т3,T5.Н4, Нб} O b. none O c. H21- Let a coin and a die be tossed; let the sample space S consists of the twelve elements: S-{HI, H2, HЗ, Н4, H5, Н6, Т1, Т2, ТЗ, Т4, T5, Т6; (i) Express explicitly the following events: A={heads and an even number appear} B={a prime number appears} C={tails and an odd number appear} (ii) Express explicitly the event that: (а) А or B oссurs A or B Select one: О а. (Н2,НЗ,H5.T2,Т3,T5.Н4, Нб} O b. none O c. H2Determine whether the events "a randomly chosen student is a male' and a randomly chosen student is studying Music' are independent, justifying your response
- 1 A telephone sales representative makes successive calls to potential customers, and the result of each call is recorded as a sale (S) or a no sale (N). Calls are continued until either two sales are made (these calls need not be consecutive), two consecutive calls result in no sale , or a total of 4 calls is made. What is the sample space for this situation. Sample Space = { }3595 You're a sociologist studying whether grocery prices are different in the inner cities than they are in the suburbs. To investigate this, you pick a random set of items (a basket of goods), and then send shoppers to buy these items at an inner city (IC) grocery, and also at a suburban (SU) grocery. You pick 35 different baskets of goods, so your secret shoppers buy 35 baskets, once at the inner city store, and once at a suburban store. Prices could be higher in the inner city because of discrimination, or they could be higher in the suburbs because of the greater disposable income. Use Excel to test the research hypothesis that inner city prices are different than the suburb's prices. The null hypothesis is that inner city prices are equal to suburban prices. You test at the alpha = 0.05 significance level. What do you conclude? Are prices the same? Who has higher prices? Group of answer choices You reject the null hypothesis; prices are different. Grocery prices are higher in…Conditional probability (reduced sample space) a) Among a group of 500 pet owners who visit the same pet store, it is found that 345 have a cat, while 375 have a dog. There are 290 of these who have both a dog and a cat. Suppose one individual is chosen at random from this group of 500 pet owners. Find the conditional probability the individual has a dog given that he or she has a cat. b,c) [use two way table from previous problem] Conditional Probability and Reduced Sample Space Consider the following two-way table representing the weather at a certain location on 300 days No Rain Little Rain (<1 in) Rain (>1 in) Sunny 175 15 0 190 Cloudy 43 32 35 110 218 47 35 300 Find each of the probabilities b) Probability of no rain given that it is a sunny day, Pr(No Rain | Sunny) c) Probability of a sunny day given that there is no rain, Pr (Sunny | No Rain)
- An integer is repeatedly selected from{1,2, . . . ,10}. Find the expected number of integers thatdo not appear in 20 selections.Discrete Probability: A bag contains 8 red, 7 green, 5 black and 10 yellow jellybeans. Six jellybeans are selected at random without replacement. a) What is the probability that at least one of the jellybeans is yellow? b) What is the expected number of black jellybeans to be selected?The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. After identifying the sample space for a couple having four children, find the probability of getting fourfour girlsgirls and nono boysboys. Identify the sample space for a couple having four children. {nothing} (Use a comma to separate answers as needed.) Find the probability of getting fourfour girlsgirls and nono boysboys.