30. Find the indicated probability. Based on mcteorological records, the will sn
ID: 3046717 • Letter: 3
Question
30. Find the indicated probability. Based on mcteorological records, the will snow in a certain town on January 1st is 0.315. Find the probabälity that in a given year it will not snow on January 1st in that town. a) 0.685 b) 0.460 c) 1.315 d) 3.175 31. Find the indicated probability. In one town, 25% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both a) 0.250 b) 0.087 c) 0.063 d) 0.500 32. Is Event B dependent or independent of Event A? B: You get salmonella poisoning. b) Independent A: You cook your chicken improperly. a) Dependent 33. You draw a card at random from a standard deck of 52 cards. Find the probability that the card is a heart given that it is black. a) 0 b) 0.5 c) 0.333 d) 0.077 c) 0.25 Bonus: I. A meal consists of a main dish, a side dish, and a dessert. How many different meals can be selected if there are 5 main dishes, 2 side dishes and 5 desserts available? A chemical engineer has 8 different treatments that she wishes to compare for effectiveness in producing a sand cast to be used in casting molten iron. She wants to compare each treatment to each of the others. How many pairwise comparisons will she have to make? That is, in how many ways can these treatments be selected two at a tim 2.Explanation / Answer
30. Answer: a) 0.685
If probability of snowing on Jan 1 = p = 0.315, the probability of not snowing on Jan 1 = 1 - p = 1 - 0.315 = 0.685.
31. Answer: c) 0.063
If probability of finding one Democrat = p = 25% = 0.25, then probability of finding two Democrats = p * p = p2 = 0.252 = 0.0625 = 0.063.
32. Answer: a) Dependent
Probability of getting salmonella poisoning is higher if chicken has been improperly cooked. On the other hand, probability of getting salmonella poisoning is lower if chicken has been properly cooked. Hence, event B is dependent on event A.
33. Answer: a) 0
A heart card is red in colour. Hence, given that a card is black, it cannot be a heart. In other words, the probability of a black card also being a heart is 0.
Bonus 1: Answer: 50 ways
The events of choosing a main dish, of choosing a side dish, and of choosing a dessert are independent. Hence, number of combinations of dishes = 5 ways of choosing a main dish * 2 ways of choosing a side dish * 5 ways of choosing a dessert = 50
Bonus 2: Answer: 28 ways
The first treatment can be chosen in 8 ways. Once chosen, the second treatment can be chosen in 8-1=7 ways. Also, order is not important in choosing. So, for example, first choosing treatment 3 and then choosing treatment 5 is same as first choosing treatment 5 and then choosing treatment 3. Hence, to avoid double counting, we have to divide by 2. So, number of ways = 8*7/2 = 28.
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