What Does Scoring a Total of 7 in Two Tosses of a Pair of Dice Involve?

[azizlwl]

Find the probability of scoring a total of 7 points (a) once, (b) at least once, (c) twice, in 2 tosses of a pair of dice.

My question.
1. What does scoring a total of 7 points mean? Is it 1+6 or 2+5 or 3+4 or 4+3 or 5+2 or 6+1

2. Is in 2 tosses of a pair of dice means that throwing 2 dices at once twice. How this relate to scoring of 7 points.

Thank you.

 

[DonAntonio]

Find the probability of scoring a total of 7 points (a) once, (b) at least once, (c) twice, in 2 tosses of a pair of dice.

My question.
1. What does scoring a total of 7 points mean? Is it 1+6 or 2+5 or 3+4 or 4+3 or 5+2 or 6+1


*** Yes ***


2. Is in 2 tosses of a pair of dice means that throwing 2 dices at once twice. How this relate to scoring of 7 points.


*** I think it actually might mean tossing a pair of dice once, or one die twice.

DonAntonio ***

Thank you.

...

 

[HallsofIvy]

Because you say specifically "2 tosses of a pair of dice" the reference is to rolling a pair of dice two different times. Each time you roll a pair of dice you can get any number from 1 to 6 (all equally likely) on the first die and 1 to 6 (all equally likely) on the second die. That means that there are 6x6= 36 equally likely combinations of two dice. Of course, the number they add to aren't equally likely. Only (1, 1) gives a sum of 2, only (6, 6) adds to 12, while (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1), 6 out of the 36 possible pairs, all add to 7. The probability a roll of two dice will add to 7 is 6/36= 1/6. Of course, that means the probability of getting anything other than a 7 rolling a pair of dice is 1- 1/6= 5/6. The probability of getting a 7 on the first roll but not on the second is (1/6)(5/6)= 5/36. The probability of getting any number other than a 7 on the first roll but a 7 on the second is (5/6)(1/6)= 5/36. So the probability of getting exactly one 7 in two rolls is (5/36)+ (5/36)= 10/36= 5/18.

All the other problems can be done similarlly.

 

[azizlwl]

Thank you

May I say that what is meant by "2 tosses of a pair of dice" is that it is the random experiment we do and all the outcomes as sample space. My understanding(easy for me to understand graphic presentation) maybe shown below
16|not7 (4 dices)
25|not7
34|not7
43|not7
52|not7
61|not 7
not 7|not 7
not 7|not 7
...
OR
not7|16
not7|25
not 7|34
...

 

[sai teja]

Thank you

May I say that what is meant by "2 tosses of a pair of dice" is that it is the random experiment we do and all the outcomes as sample space. My understanding(easy for me to understand graphic presentation) maybe shown below
16|not7 (4 dices)
25|not7
34|not7
43|not7
52|not7
61|not 7
not 7|not 7
not 7|not 7
...
OR
not7|16
not7|25
not 7|34
...

u r right