two dice are thrown at random, what is the probability that the numbers will be a product of 5?

Question

.........and why

Answer 1

there are 6 x 6 = 36 possibilities.

Multiples of 5 are 5 and 10
5 can be (1,4) (4,1) (2,3) or (3,2)
10 can be (4,6), (6,4), (5,5)

so it is 7 out of 36 possibilities

Prob = 7/36

Answer 2

By "product of 5," do you mean: "multiple of 5"?

The lowest value you can get with two dice is: 2
The highest value you can get with two dice is: 36
So the only multiples of 5 you can get from the two dice are between 2 and 36, which are: 5, 10, 15, 20, 25, 30 (and not 35 because I'm assuming that the dice that are being thrown are regular, cubic, 6-sided dice, and if a '35' is possible, then there must be a 7th side - 5 * 7)

In other words, there are six multiples of 5 that you can obtain with two dice, but there are two dice, so there are two ways that you can obtain each multiple. For example, for '5,' you can have (1 * 5) or (5 * 1); for 10, you can have (2 * 5) or (5 * 2), and so on. So really, there are 12 ways that you can obtain a product that is a multiple of 5 with two dice.

There are a total of 6^2 = 36 total combinations of numbers that you can obtain with two dice.

So the probability of obtaining a product of 5 with two dice is:
12:36 = 1:3

Therefore, the probability of obtaining a product (multiple) of 5 with two 6-sided dice is, 1:3.

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Or maybe I misunderstood the question, if you meant:
What is the probability of obtaining two dice that (when mulitplied together) results in a product of 5? Then this is the solution:

With two dice, there are only two ways to obtain a product of 5, which is (1 * 5) or (5 * 1).
With two dice there are a total of 6^2 = 36 combinations.

Therefore, the probability of obtaining two dice that (when mulitplied together) results in a product of 5, is 2:36, which is also, 1 : 18.

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Or if you meant to ask: What is the probability of obtaining the sum of two dice that is also a multiple of 5? Then everyone else is indeed correct, the answer should be,
7 : 36.

Answer 3

Two numbers that are product of 5 and you can get with two dice are 5 and 10. To get 5 or 10 you need :

case 1: 4 and 1
or
case 2: 2 and 3
or
case 3: 1 and 4
or
case 4: 3 and 2
or
case 5: 6 and 4
or
case 6: 5 and 5
or
case 7: 4 and 6

(assume the first number is what you get on first dice and the second number is what you get on the second dice)

The probability to get 4 is 1/6 because the dice has 6 sides and only one side with 4 on it.
The probability to get 1 is also 1/6 for the same reason mentioned above.
The probability to get 4 and 1 is the product of the two probabilities which is 1/36

You can apply the reasoning above for every case, so the probability for every case is 1/36.

To get the total for probability of getting sum of 5 or 10 you have to add up the probabilities of all the cases because each one could give you the answer. The rule of thumb is whenever you have "and" you multiply and whenever you have "or" you add. So the answer will be 7/36.

Answer 4

Your question contains the ambiguous phrase "product of 5". If you meant the sum of the dice is a multiple of five (i.e. 5 or 10) the question should have been worded that way.

I assume you meant the product of the numbers on the two dice is five. In that case the two possibilities are:

{1, 5} and {5, 1}.

There are 6² = 36 possible combinations.

So the probability in question is

P(5) = 2/36 = 1/18

Answer 5

Assume that one die is green and the other is red.

Green ace, red four
Green two, red three
Green three, red two
Green four, red ace.
Green four, red six.
Green five, red five
Green six, red four

There are 36 possible pairs (six options for red, six for green), and 7 chances that the number displayed will be a product of 5.

Consequently, the odds are 7 in 36.

(If 5 itself is not considered "a product of five", then the odds would be 1 in 12 - with three winning combinations - R6G4, R5G5, R4G6 - out of 36)

Answer 6

When two dies are thrown,
no. of possible outcomes of first dice=6
no. of possible outcomes of second dice=6
Total no. of possible outcomes when two dies are thrown=6x6=36
There are only 2 cases in which the nos. will give a product of five-when 5 is the outcome of the first dice and 1 is the outcome of the second or 1 is the outcome of the first dice and 5 is the outcome of the second.
Probability=(no.of possible cases)/(Total no. of possible outcomes)=2/36=1/18.

Answer 7

Rolling 2 dice gives 36 possible outcomes.
Outcomes giving products of 5 are:
(1,4) (2,3) (3,2) (4,1) (4,6) (5,5) (6,4)
ie 7 outcomes
P( product of 5) = 7 / 36

Answer 8

3/12

Answer 9

2 of 21 there 21 approaches it could artwork one million way of having a 12 one million way of having a eleven 2 approaches of having a ten 2 approaches of having a 9 3 approaches of having a 8 3 approaches of having a 7 3 approaches of having a 6 2 approaches of having a 5 2 approaches of having a 4 one million way of having a three one million way of having a 2

Answer 10

There are 6*6=36 equally likely, mutually exclusive and exhaustive outcomes.
The outcome of product of 5 is (1,4), (2,3), (3,2), (4,1), (4,6), (5,5), (6,4). I.e there are 7 outcomes.
P(the numbers of product of 5) = 7/36.