Question

In: Statistics and Probability

16. What is the (approximate) probability that Die1+Die2+Die3=10? a. The probability is approximately 5%. b. The...

16. What is the (approximate) probability that Die1+Die2+Die3=10? a. The probability is approximately 5%. b. The probability is approximately 10%. c. The probability is approximately 20%. d. The probability is approximately 25%. 17. What is the (approximate) probability that Die1+Die2+Die3>10? a. The probability is approximately 25%. b. The probability is approximately 35%. c. The probability is approximately 50%. d. The probability is approximately 75%. 18. What is the (approximate) probability that Die1+Die2>9? Careful: You need to create another column (and histogram) based on the first two dice or to argue directly by listing all possible outcomes! a. The probability is approximately 5%. b. The probability is approximately 15%. c. The probability is approximately 25%. d. The probability is approximately 35%.

Solutions

Expert Solution

The total possible outcomes are 216.

Total possibe outcomes for rolling three dice
1,1,1 1,1,2 1,1,3 1,1,4 1,1,5 1,1,6
1,2,1 1,2,2 1,2,3 1,2,4 1,2,5 1,2,6
1,3,1 1,3,2 1,3,3 1,3,4 1,3,5 1,3,6
1,4,1 1,4,2 1,4,3 1,4,4 1,4,5 1,4,6
1,5,1 1,5,2 1,5,3 1,5,4 1,5,5 1,5,6
1,6,1 1,6,2 1,6,3 1,6,4 1,6,5 1,6,6
2,1,1 2,1,2 2,1,3 2,1,4 2,1,5 2,1,6
2,2,1 2,2,2 2,2,3 2,2,4 2,2,5 2,2,6
2,3,1 2,3,2 2,3,3 2,3,4 2,3,5 2,3,6
2,4,1 2,4,2 2,4,3 2,4,4 2,4,5 2,4,6
2,5,1 2,5,2 2,5,3 2,5,4 2,5,5 2,5,6
2,6,1 2,6,2 2,6,3 2,6,4 2,6,5 2,6,6
3,1,1 3,1,2 3,1,3 3,1,4 3,1,5 3,1,6
3,2,1 3,2,2 3,2,3 3,2,4 3,2,5 3,2,6
3,3,1 3,3,2 3,3,3 3,3,4 3,3,5 3,3,6
3,4,1 3,4,2 3,4,3 3,4,4 3,4,5 3,4,6
3,5,1 3,5,2 3,5,3 3,5,4 3,5,5 3,5,6
3,6,1 3,6,2 3,6,3 3,6,4 3,6,5 3,6,6
4,1,1 4,1,2 4,1,3 4,1,4 4,1,5 4,1,6
4,2,1 4,2,2 4,2,3 4,2,4 4,2,5 4,2,6
4,3,1 4,3,2 4,3,3 4,3,4 4,3,5 4,3,6
4,4,1 4,4,2 4,4,3 4,4,4 4,4,5 4,4,6
4,5,1 4,5,2 4,5,3 4,5,4 4,5,5 4,5,6
4,6,1 4,6,2 4,6,3 4,6,4 4,6,5 4,6,6
5,1,1 5,1,2 5,1,3 5,1,4 5,1,5 5,1,6
5,2,1 5,2,2 5,2,3 5,2,4 5,2,5 5,2,6
5,3,1 5,3,2 5,3,3 5,3,4 5,3,5 5,3,6
5,4,1 5,4,2 5,4,3 5,4,4 5,4,5 5,4,6
5,5,1 5,5,2 5,5,3 5,5,4 5,5,5 5,5,6
5,6,1 5,6,2 5,6,3 5,6,4 5,6,5 5,6,6
6,1,1 6,1,2 6,1,3 6,1,4 6,1,5 6,1,6
6,2,1 6,2,2 6,2,3 6,2,4 6,2,5 6,2,6
6,3,1 6,3,2 6,3,3 6,3,4 6,3,5 6,3,6
6,4,1 6,4,2 6,4,3 6,4,4 6,4,5 6,4,6
6,5,1 6,5,2 6,5,3 6,5,4 6,5,5 6,5,6
6,6,1 6,6,2 6,6,3 6,6,4 6,6,5 6,6,6

The probability of sum 10 P( Die1+Die2+Die3=10)

Total possibe outcomes for Die1+Die2+Die3=10
3,6,1 2,6,2 1,6,3 1,5,4 1,4,5 1,3,6
4,5,1 3,5,2 2,5,3 2,4,4 2,3,5 2,2,6
5,4,1 4,4,2 3,4,3 3,3,4 3,2,5 3,1,6
6,3,1 5,3,2 4,3,3 4,2,4 4,1,5
6,2,2 5,2,3 5,1,4
6,1,3

There are 27 possible outcomes for Die1+Die2+Die3=10

= (possible outcomes for Die1+Die2+Die3=10)/(The total possible outcomes) = 27/216 = 12.5%

Probability is approximately 10%.

Probability that Die1+Die2+Die3>10

Total possibe outcomes for Die1+Die2+Die3=10
1,4,6 1,5,5 1,6,4 2,6,3 3,6,2 4,6,1
1,5,6 1,6,5 2,5,4 3,5,3 4,5,2 5,5,1
1,6,6 2,4,5 2,6,4 3,6,3 4,6,2 5,6,1
2,3,6 2,5,5 3,4,4 4,4,3 5,4,2 6,4,1
2,4,6 2,6,5 3,5,4 4,5,3 5,5,2 6,5,1
2,5,6 3,3,5 3,6,4 4,6,3 5,6,2 6,6,1
2,6,6 3,4,5 4,3,4 5,3,3 6,3,2
3,2,6 3,5,5 4,4,4 5,4,3 6,4,2
3,3,6 3,6,5 4,5,4 5,5,3 6,5,2
3,4,6 4,2,5 4,6,4 5,6,3 6,6,2
3,5,6 4,3,5 5,2,4 6,2,3
3,6,6 4,4,5 5,3,4 6,3,3
4,1,6 4,5,5 5,4,4 6,4,3
4,2,6 4,6,5 5,5,4 6,5,3
4,3,6 5,1,5 5,6,4 6,6,3
4,4,6 5,2,5 6,1,4
4,5,6 5,3,5 6,2,4
4,6,6 5,4,5 6,3,4
5,1,6 5,5,5 6,4,4
5,2,6 5,6,5 6,5,4
5,3,6 6,1,5 6,6,4
5,4,6 6,2,5
5,5,6 6,3,5
5,6,6 6,4,5
6,1,6 6,5,5
6,2,6 6,6,5
6,3,6
6,4,6
6,5,6
6,6,6

There are 108 possible outcomes for Die1+Die2+Die>10

The probability of sum>10 P( Die1+Die2+Die3>10) = 108/216 = 50%

Approximate Probability that Die1+Die2+Die3>10 is 50%.

For rolling two dice

The total possible outcomes are 36

Total possibe outcomes for rolling two dice
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6

probability that Die1+Die2>9

The posible outcome are (4,6),(5,5),(5,6),(6,4),(6,5),(6,6)

Possible outcome for Die1+Die2>9 are 6

probability that Die1+Die2>9 = 6/36 = 16.6%

approximately 15%.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

If 10% of the general population smokes, what is the approximate probability that fewer than 100...
If 10% of the general population smokes, what is the approximate probability that fewer than 100 in a random sample of 928 people are smoker?
Using the normal approximation, find the approximate probability of at most 16 successes of 40. You...
Using the normal approximation, find the approximate probability of at most 16 successes of 40. You may need to consult your z table or the shiny app
a) What is the probability of rolling a 5 with a balanced die? b) Find the...
a) What is the probability of rolling a 5 with a balanced die? b) Find the number of ways in which a person can select 3 stocks from a list of 5 stocks? c) What is probability of drawing a 5 from a well shuffled deck of 52 playing cards? d) In how many ways can a principal choose 3 of 45 members to review a student grade appeal?
COMMON STOCK A COMMON STOCK B PROBABILITY RETURN PROBABILITY RETURN 0.25 10​% 0.20 −5​% 0.50 15​%...
COMMON STOCK A COMMON STOCK B PROBABILITY RETURN PROBABILITY RETURN 0.25 10​% 0.20 −5​% 0.50 15​% 0.30     6% 0.25 18​% 0.30 16% 0.20 22% expected rate of return and risk​) Summerville Inc. is considering an investment in one of two common stocks. Given the information in the popup​ window: ​, which investment is​ better, based on the risk​ (as measured by the standard​ deviation) and return of​ each? a. The expected rate of return for Stock A is ​%. ​(Round...
the probability of getting a single pair in a poker hand of 5 cards is approximately...
the probability of getting a single pair in a poker hand of 5 cards is approximately .42. Find the approximate probability that out of 1000 poker hands there will be at least 450 with a single pair.
Suppose that we roll a die 166 times. What is the approximate probability that the sum...
Suppose that we roll a die 166 times. What is the approximate probability that the sum of the numbers obtained is between 544 and 606, inclusive. (if possible, could you explain the steps/ state theorems used). Thank you :)
Solution Absorbance [Fe(SCN)2+]eq B-1 0.060 1.4*10-5 B-2 0.151 3.8*10-5 B-3 0.323 8.07*10-5 B-4 0.381 9.5*10-5 B-5...
Solution Absorbance [Fe(SCN)2+]eq B-1 0.060 1.4*10-5 B-2 0.151 3.8*10-5 B-3 0.323 8.07*10-5 B-4 0.381 9.5*10-5 B-5 0.427 1.06*10-4 Solution Vol of 0.002 M Fe3+ Volume of 0.002 M SCN- Volume of H2O B-1 5.0 mL 1.0 mL 5.0 mL B-2 5.0 mL 2.0 mL 4.0 mL B-3 5.0 mL 3.0 mL 3.0 mL B-4 5.0 mL 4.0 mL 2.0 mL B-5 5.0 mL 5.0 mL 1.0 mL 2. Determine the equilibium concentration of each of the reactants and products in...
(a) What is the probability that a 5-card poker hand has at least three spades? (b)What...
(a) What is the probability that a 5-card poker hand has at least three spades? (b)What upper bound does Markov’s Theorem give for this probability? (c)What upper bound does Chebyshev’s Theorem give for this probability?
(a) What is the probability that a 5-card poker hand has at least three spades? (b)What...
(a) What is the probability that a 5-card poker hand has at least three spades? (b)What upper bound does Markov’s Theorem give for this probability? (c)What upper bound does Chebyshev’s Theorem give for this probability?
a) What is the probability that a 5-card poker hand has at least three spades? (b)What...
a) What is the probability that a 5-card poker hand has at least three spades? (b)What upper bound does Markov’s Theorem give for this probability? (c)What upper bound does Chebyshev’s Theorem give for this probability? the other questions have the wrong solution, so please help.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT