If you use round, to 6 decimal places for this assignment 1. (9 points) In the g
ID: 3302279 • Letter: I
Question
If you use round, to 6 decimal places for this assignment 1. (9 points) In the game of Yahtzee, five regular six-sided dice are thrown. The results are cate- gorized in several different ways. In one roll of the five dice, find the probability of getting: (if you use decimals, round to 6 decimal places A) a Yahtzee (that is, all five dice are the same, such as 2-2-2-2-2) B) a large straight (that is, all are in order, such as 2-3-4-5-6) C) a full house (that is, three of one number and two of another, such as 1-1-1-2-2. A 1-1-1-1-1 is NOT considered a full house)Explanation / Answer
Please note that the total number of combinations possible in throwing 5 dice is 6*6*6*6*6 = 7776
A. The different Yahtzees are 11111, 22222, 33333, 44444, 55555 and 66666. They are 5 in number.
Probability of getting a Yahtzee = 5/7776 = 0.000643.
B. The different straights are 12345, 23456, 54321, 65432. They are 4 in number.
Probability of getting a straight = 4/7776 = 0.000514.
C. The threes can come in 6 ways and the twos in 5 ways.
The threes can occupy 5 places in 5C3 = 10 ways. The remaining are to be occupied by the twos.
=> Total full houses = 6 * 5 * 10 = 300
Probability of getting a full house = 300 / 7776 = 0.038580