Question 1139354: A blue die and a red die are rolled simultaneously. A two-digit number is formed by noting the outcomes: the blue die giving the tens digit and the red die giving the units digit. E.g
3 on the blue die and 5 on the red die give the two-digit number 35.
a) Make a table showing all the possible outcomes.
b) What is the probability of obtaining a two-digit number which is
i) greater than 30.
ii) exactly divisible by 11.
iii) prime?
c) What is the probability of obtaining a two-digit number that is either a perfect square or exactly divisible by 7?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
I don't know what it is you need help with on this; the instructions seem straightforward, and the questions are simple....
a) The possible outcomes are all the 2-digit numbers with both digits between 1 and 6 (inclusive). There are 6*6=36 such numbers. You can make the table.
b) As an example of these questions, the 2-digit prime numbers with both digits between 1 and 6 are 11, 13, 23, 31, 41, 43, 53, 61. That's 8 numbers; the probability that one of the outcomes randomly selected is prime is 8/36 = 2/9.
You can work the other problems similarly.
Answer by ikleyn(52858)  (Show Source):
You can put this solution on YOUR website! .
Although the problem includes MANY question, it is SIMPLE due to its nature.
Nevertheless, there are some useful things to learn while solving this problem,
and I am going to teach you to these useful things.
There are three such things: one is on how to organize your data in the solution;
the other is on how to organize you thoughts; and the third is how to present the solution itself.
The method and the way on how to do it is to create an appropriate table.
I created this table below for you.
T A B L E
blue red two-digit two-digit two-digit two-digit perfect square
die die number numbers > 30 number div.by 11 prime numbers or div. by 7
(i) (ii) (iii) (c)
1 1 11 * *
1 2 12
1 3 13 *
1 4 14 *
1 5 15
1 6 16 *
2 1 21 *
2 2 22 *
2 3 23 *
2 4 24
2 5 25 *
2 6 26
3 1 31 * *
3 2 32 *
3 3 33 * *
3 4 34 *
3 5 35 * *
3 6 36 * *
4 1 41 * *
4 2 42 * *
4 3 43 * *
4 4 44 * *
4 5 45 *
4 6 46 *
5 1 51 *
5 2 52 *
5 3 53 * *
5 4 54 *
5 5 55 * *
5 6 56 * *
6 1 61 * *
6 2 62 *
6 3 63 * *
6 4 64 * *
6 5 65 *
6 6 66 * *
the number of 4*6 = 24 6 8 10
favored outcomes
the probability 24/36=2/3 6/36=1/6 8/36=2/9 10/36 = 5/18
under the question
The lessons to learn from my post are THESE :
When you organize your data by a reasonable way, it may help you to save your time and efforts while solving a problem;
It may prevent you of doing repeating operations;
It provides you the way to present your solution to others and educate yourself and others (yours pupils).
Solved and completed.
------------------------
To see other similar solved problems on rolling dice, look into the lesson
- Rolling a pair of fair dice
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Solved problems on Probability".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
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