Question

when two dice are rolled what is the probability that (1) the sum of the numbers at least 10 (2) the product of number is 8 (3) both are even
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Answer 1

Answer:

1) 1/2

2)1/6

Step-by-step explanation:

S= {1 ,2,3,,5,46,1,2,3,4,5,6}

P(A)= A/S

     = 6/12

      = 1/2

Answer 2

Probability

Step-by-step explanation:

A dice has 6 faces.

Two dice are rolled.

So the total possible outcomes are as follows:

    Dice 1, Dice 2

• 1, 1
• 1, 2
• 1, 3
• 1, 4
• 1, 5
• 1,6
• 2, 2
• 2, 3
• 2, 4
• 2, 5
• 2, 6
• 3, 3
• 3, 4
• 3, 5
• 3, 6
• 4, 4
• 4. 5
• 4, 6
• 5, 5
• 5, 6
• 6, 6

So the total number of possible outcomes is 21.

Now,

We have to find the probability of the following:

(1) The probability that sum of the numbers is at least 10.

The total possible outcomes that has the sum of the numbers is at least 10 are 4:

1. (4, 6)
2. (5, 5)
3. (5, 6)
4. (6, 6)

So, the probability that sum of the numbers is at least 10 is  $\frac{4}{21}$.

(2) The probability that the product of numbers is 8.

The total possible outcome that has the product of numbers is 8 is 1 :

1. (2,4)

So, the probability that  the product of numbers is 8 is $\frac{1}{21}$.

(3) The probability that both the numbers are even.

The total possible outcome so that both the numbers are even are 6 :

1. (2, 2)
2. (2, 4)
3. (2, 6)
4. (4, 4)
5. (4, 6)
6. (6, 6)

So, the probability that both the numbers are even is $\frac{6}{21}$.