Question

Two dice are thrown at the same time find the probability that the sum of two numbers appears on the face is more than or equal to 9

Answer 1

${ \pink{ \huge{bonjour}}}$

Here's ur answer=>

Two dice are thrown,means that total probability of the two dices is=6×6

=36.

Probability of sum of 9 or more=>

Total favourable outcomes=(3,6) , (4,5) , (4,6) , (5,4) , (5,5) , (5,6) , (6,3) , (6,4) , (6,5), (6,6).

Total number of favourable outcomes=10

Probability=

$= \frac{total \: number \: of \: favourable \: outcomes}{total \: outcomes}$

$= \frac{10}{36}$

$= \frac{5}{18}$

Hence your answer is 5/18.

Hope this helps ☺

✌Divjot✌

Answer 2

The probability that the sum of two numbers appears on the face is more than or equal to 9 is 5/18

Given :

Two dice are thrown at the same time

To find :

The probability that the sum of two numbers appears on the face is more than or equal to 9

Solution :

Step 1 of 3 :

Find total number of possible outcomes

Here it is given that two dice are thrown at the same time

So the event points are

= { (1,1), (1,2), (1,3), (1,4),(1,5),(1,6),(2,1), (2,2), (2,3), (2,4),(2,5),(2,6),(3,1), (3,2), (3,3), (3,4),(3,5),(3,6),(4,1), (4,2), (4,3), (4,4),(4,5),(4,6),(5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2), (6,3), (6,4),(6,5),(6,6)}

So the total number of possible outcomes = 36

Step 2 of 3 :

Find the total number of possible outcomes for the event

Let A be the event that the sum of two numbers appears on the face is more than or equal to 9

Since the sum of two numbers appears on the face is more than or equal to 9

So sum will be one of 9 , 10 , 11 , 12

When sum is 9 the points are (3,6),(4,5),(5,4),(6,3)

When sum is 10 the points are (4,6),(5,5),(6,4)

When sum is 11 the points are (5,6), (6,5)

When sum is 12 the points are (6,6)

Therefore the event points for the event A are

(3,6),(4,5),(5,4),(6,3),(4,6),(5,5),(6,4), (5,6), (6,5),(6,6)

So the total number of event points for the event A is 10

Step 3 of 3 :

Find the probability

The probability that the sum of two numbers appears on the face is more than or equal to 9

$\sf{ =P(A) }$

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf{ = \frac{10}{36} }$

$\displaystyle \sf{ = \frac{5}{18} }$

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