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(5 marks) From a population of individuals the following statistics are reported: 25% watch football (event F) 40% watch hockey (event H) 30% watch curling (event C...

Question

(5 marks) From a population of individuals the following statistics are reported: 25% watch football (event F) 40% watch hockey (event H) 30% watch curling (event C) 15% watch football and hockey 20% watch hockey and curling 10% watch football and curling 5% watch all of these sports What proportion of individuals watch exactly one of these sports?

(5 marks) From a population of individuals the following statistics are reported: 25% watch football (event F) 40% watch hockey (event H) 30% watch curling (event C) 15% watch football and hockey 20% watch hockey and curling 10% watch football and curling 5% watch all of these sports What proportion of individuals watch exactly one of these sports?



Answers

Sports In survey of students about favorites, the results include 22 who like tennis, 25 who like football, 9 who like tennis and football, 17 who like tennis and baseball, 20 who like football and baseball, 6 who like all three sports, and 4 who like none of the sports. How many students like only tennis and football? How many students like only tennis and baseball? How many students like only baseball and football?

We know that about 20% of the population watches both news and soap operas, so let's call this probability of news and soaps equals zero 0.25 In order to convert from a percent to a decimal, take your decimal point and move it over to the left two spaces. We also know that 75% of the population watches the news. So let's call this the probability of end or news equals zero 0.75 Because again, to convert from a percent to a decimal, move your decimal place over two spaces to the left. We're wondering about what is the probability of someone watching soap operas, knowing that they already watched the news. Let's use our multiplicity of property for this. We know that the probability of news and soap operas is equal to the probability of just the News Times the probability of watching soap operas. Given that you already watched the news, let's fill in our information. We know that the 1st 1 is 0.25 or 25%. We also know that the probability of the news is 0.75 for 75%. This is being multiplied with what we're looking for. The probability of watching soap operas Given that you watch the news well, there's multiplication going on between these two values. So in order to get what we want alone, we have to divide both sides by 0.75 When you divide 0.25 by 0.75 you get 1/3, since both are divisible by 0.25 1/3 or 1/3 as a decimal 0.3 three. Repeating thus the probability of someone watching soap operas given that they already watched the news is 0.3 three repeated, or about 33 0.33333%.

All right. This question deals was sampling from a distribution of Size 10 where seven people prefer football while three prefer basketball. So first it wants for party the probability that a sample of two people out of three prefer football and that plugging into her hyper geometric formula we have. They're seven people that like football, and we want two of them. And then there are three people that prefer basketball, and we want one of them and they're 10 people, and we're choosing three of them for our sample. And that is 0.52 five. And then Part B asks, What is the probability that X equals two or X equals three, which is the same thing as P of two, which we already know, plus p of three, Which they're seven. That like football, we want three of them. There are three people that prefer basketball. We want zero of them and there are 10 people to pick from and we want three of them. And that works out to be 0.8167 because recall that this is 0.5 to 5, as calculated in party

Let's see denotes the set of people who like cricket. And T denotes the set of people who like tennis. So here. Thank you. In number of people in C. Union T. Equal to 65. Number of people in C. Equal to 40. Number of people in C. Intersection T. Equal to then. So here we have to find a number of people like Dennis only and not kick it. And how many like tennis? So here we have a formula for this. Number of people in C. Union T. Equal to number of people in C. Place a number of people in P negative number of people in C intersection T. So now here we put the values which is given 65 equal to 40. It was number of pupils in T. Negative. And so now we simplify this and here we get number of people in T. Equal to 35. Therefore 35 people like Dennis. So it is our answer. Now we have to find number of people like tennis only. So now we have a formula for this B. Negative C. The union the intersection C. Equal to T. And P. Native C intersection T intersection C. Equal to why? So here number of people M. T. Equals number of people in T minus see plus number of people mt intersection C. So here we put the value of number of people in T. Which is 35 equal to and 18 minus C. Plus number of people N. T intersection C. Is 10. So we put here and now we simplify this. So here we get number of people in T minus C equal to 25 and therefore 25 people. Well I only tennis. So it is a final answer.

In this problem. There are 80 students in a class. So daughter is equal to 80 60 play football. 53 play hockey and 35 play both of the games. Lets me go right back home for this. This is for football and this is for what? Let the blue region which is this region. We denoted us. The blue region at the green region, B. C. And the center reason me both is equal stew the now 60 play football. Football is played with the blue and the red reason. So A plus B is equal to 60. Also 53 play hockey. Hockey's by the region, Green and red. So B plus C. Has given us 53 35 play both of the games. It is the red which is B which is 35. Now, first thing, how many students do not play any of them two games. Let us solve this. First B is 35 means that see is 53 minus 35 which is 18 and he is 16 minus 35 inches 25. So players who play either football or hockey will be mounted by the region A plus B plus C, which is 25 plus 35 plus 18. This is I think. What 70? Yeah. So the number of players who do not play any of this is the cookies minus 78 which is a t minus 78 which is that's the good part two play only hockey, but not football. So that region of only hockey and football is done. Green Reason, which is nothing but sea, which is it did.


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