a red die and a blue die are thrown at the same time. list all the possible outcomes in a systematic way. find the probability of obtaining: (a) a total of ten (b) a total of 12 (c) a total less than 6 (d) the same number on both dice (e) a total more than 9. what is the most likely total?
Answers
Answer:
A red and a blue die are thrown. Both dice are loaded (that is, not all sides are equally likely). Rolling a 2 with the red die is twice as likely as rolling each of the other five numbers and rolling a 4 with the blue die is twice as likely as rolling each of the other five numbers.
a. What is the probability of each outcome of the red die?
b. What is the probability of each outcome of the blue die?
c. What is the probability that the sum of the numbers on the two dice is 6?
My attempt
a. Red die probability
1- 1/7
2- 2/7
3- 1/7
4- 1/7
5-1/7
6- 1/7
b. Blue die probability
1 - 1/7
2 - 1/7
3 - 1/7
4 - 2/7
5 - 1/7
6 - 1/7
c) Sum of nos. as 6 for both die
Various possible combinnations (Red, Blue) with probabilities as below
(1,5) - (1/7(1/7)
(2,4) - (2/7)(2/7)
(3,3) - (1/7)(1/7)
(4,2) - (1/7)(1/7)
(5,1) - (1/7)(1/7)
Overall probability - 4. (1/7)2 + (2/7)2 = 16.32%