Question

Dice can be used in a multitude of ways. Let's have some fun rolling dice as we practice working with probabilities. (e) Roll a pair of dice 36 times. Record the pairs and their corresponding sums in the table provided. Then use the sum information to complete the probability table. (f) Evaluate the following probabilities from your table. i. P(sum of 4 or sum of 12) ii. P(sum of 9 or an even sum) iii. P(doubles) iv. P(an odd sum or a sum greater than 7) v. P(a prime number sum) vi. P(sum of 2) (g) Make a bar graph of your probabilities in part (f). Label the vertical axis in fractional form (1/36, 2/36, 3/36 ... 8/36). (h) Make a bar graph of your probabilities shown in the table in part (e). Label the vertical axis in fractional form (1/36, 2/36, 3/36 ... 8/36). (i) Describe the shape of the graphs in (g) and (h). 

          Dice can be used in a multitude of ways. Let's have some fun rolling dice as we practice working with probabilities.

(e) Roll a pair of dice 36 times. Record the pairs and their corresponding sums in the table provided. Then use the sum information to complete the probability table.

(f) Evaluate the following probabilities from your table.
i. P(sum of 4 or sum of 12)
ii. P(sum of 9 or an even sum)
iii. P(doubles)
iv. P(an odd sum or a sum greater than 7)
v. P(a prime number sum)
vi. P(sum of 2)

(g) Make a bar graph of your probabilities in part (f). Label the vertical axis in fractional form (1/36, 2/36, 3/36 ... 8/36).

(h) Make a bar graph of your probabilities shown in the table in part (e). Label the vertical axis in fractional form (1/36, 2/36, 3/36 ... 8/36).

(i) Describe the shape of the graphs in (g) and (h).
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Dice can be used in a multitude of ways. Let's have some fun rolling dice as we practice working with probabilities. (e) Roll a pair of dice 36 times. Record the pairs and their corresponding sums in the table provided. Then use the sum information to complete the probability table. (f) Evaluate the following probabilities from your table. i. P(sum of 4 or sum of 12) ii. P(sum of 9 or an even sum) iii. P(doubles) iv. P(an odd sum or a sum greater than 7) v. P(a prime number sum) vi. P(sum of 2) (g) Make a bar graph of your probabilities in part (f). Label the vertical axis in fractional form (1/36, 2/36, 3/36 ... 8/36). (h) Make a bar graph of your probabilities shown in the table in part (e). Label the vertical axis in fractional form (1/36, 2/36, 3/36 ... 8/36). (i) Describe the shape of the graphs in (g) and (h).
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Transcript

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00:01 So i'm going to set up part of this problem for you and part i'll leave for you.
00:03 But you had to roll a pair of dice 36 times.
00:06 And you can go ahead and roll those dice.
00:08 Or you can use this technique where you use rand, int, that's under math and probability.
00:14 And this would be rolling two dice.
00:15 And then you can write down your outcomes.
00:17 Another thing you can do is you can go randint, 1 to 6, and get 36 of those rolls and store them into list 1.
00:26 And then do this again, rand -aunt, and store those roles into list two.
00:33 There'll be different roles.
00:35 And then you can have your list 3 be the sum, and then you'll have those sums, and then you can tabulate.
00:40 You can also make a little bar graph on your calculator to see what that is and trace along to do these counts.
00:46 That's what i actually did.
00:48 So now we need to find these probabilities from the table.
00:52 Obviously, this is going to be just a sample.
00:55 This is not, this is experimental and it will vary.
00:59 So this is what i happen to get.
01:01 So for me, out of 36, the likelihood of a sum of four or 12 was 4 plus 1 is 536.
01:11 The probability of a sum of 9.
01:14 Let's see how we can the sum of 9.
01:16 I had 6 of those or even, and those will be mutually exclusive.
01:20 And so i have 2, 4, 6, 8, 10, 3.
01:25 12.
01:26 I need to add those up.
01:27 So that's 5 plus 3 is 8 plus 4 is 12 plus 6 is 18 plus 1 is 19.
01:34 So i would have 25 out of 36.
01:38 Now the doubles...
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