If you roll a die (singular of dice), what is the probability you will roll: (a) a 6? (b) an even number? (c) a number divisible by 3? (d) if you roll a pair of dice, what is the probability that you will roll two 6s? (e) an even number on one and an odd number on the other? (f) matching numbers? (g) two numbers both over 4?

A dice generally has 6 sides, numbered from 1 - 6. Answer all the following:

(a) There is only one side number 6 out of the 6 sides. The probability would be 1/6.

(b) There are 3 sides that have an even number (2, 4, 6). The probability would be 3/6. Simplify. Divide 3 to both the numerator and denominator:

(3/6)/(3/3) = 1/2

1/2 would be your simplified answer.

(c)There are 2 numbers divisible by 3 (3, 6). The probability would be 2/6. Simplify. Divide 2 from both the numerator and denominator:

(2/6)/(2/2) = 1/3

1/3 would be your simplified answer.

(d) You have 2 dices. You are trying to roll for 2 6's. There are one 6 in each dice. Remember, one dice has the probability of 1/6 to get a 6. The two dices are independent variables, meaning that one dice would not affect the other. Multiply the two fractions together:

(1/6)(1/6) = (1 * 1)/(6 * 6) = 1/36

1/36 would be your answer.

(e) You have 2 dices. One has to roll a odd number, while the other a even number.

Remember, there are 6 sides:

1, 3, 5 are the odd sides (3 odd sides in all)

2, 4, 6 are the even sides (3 even sides in all)

You have a 1/2 chance of rolling an odd number on one dice, and 1/2 a chance to roll an even number on the other. Multiply the two numbers together:

(1/2)(1/2) = (1 * 1)/(2 * 2) = 1/4

1/4 is your answer.

(f) You are trying to roll matching numbers. Take only ONE pair of matching numbers. (for example, 1). In this case, it is the same as (d). Multiply the probability of getting 1 (out of 6 sides) with two dices worth of sides:

(1/6)(1/6) = (1 * 1)/(6 * 6) = 1/36

1/36 would be your answer.

(g) You are rolling for numbers over 4 for both of the dices (5, 6) Remember, there are 6 side in all. The fraction for numbers over 4 on a dice is 2/6, or 1/3. You have 2 dices, so multiply two fractions:

(1/3)(1/3) = (1 * 1)/(3 * 3) = 1/9

1/9 would be your answer.

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