Answer:
(a)=1/4,(b)=1/512
Explanation:
(a) The two dice each have four possible outcomes, and the total number of possible outcomes when the two dice are thrown is 4 x 4 = 16. To determine the most likely total score, we need to find the sum that has the highest probability of occurring.
To do this, we can create a table that shows all the possible outcomes and their corresponding probabilities:
Dice 1 Dice 2 Total Probability
1 1 2 1/16
1 2 3 1/8
1 3 4 1/16
1 4 5 1/8
2 1 3 1/8
2 2 4 1/16
2 3 5 1/8
2 4 6 1/16
3 1 4 1/16
3 2 5 1/8
3 3 6 1/16
3 4 7 1/8
4 1 5 1/8
4 2 6 1/16
4 3 7 1/8
4 4 8 1/16
From the table, we can see that the most likely total score is 5, which occurs with a probability of 1/8 + 1/8 = 1/4.
(b) The probability of obtaining a specific score on three successive throws is the product of the probabilities of obtaining that score on each throw, assuming that the dice are fair and independent. The most likely total score is 5, so we will calculate the probability of obtaining a total score of 5 on each throw and then multiply the probabilities together.
The probability of obtaining a total score of 5 on one throw is 1/8, as we can see from the table above. Therefore, the probability of obtaining a total score of 5 on three successive throws is (1/8) x (1/8) x (1/8) = 1/512.