If two dice are thrown what is the probability that the sum is 7

Solution:

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What is the probability of rolling two dice and getting a sum of 7
The correct option is D. 16Given,Sample space for rolling a pair of dice = S { (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) }⇒ Total number of outcomes = 36From the sample space, (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1) gives sum of 7.⇒ Number of favourable outcomes = 6Probability of an event, P(E) = number of favourable outcomestotal number of outcomesP ( getting sum 7) =636=16 Therefore, the probability of getting a sum of 7 on rolling a pair of dice is 16.
What is the probability that the sum of two dice is 7?
What is the probability of getting a sum of 7 dice are thrown?
What's the probability of rolling a 7 with two dice?

Sample space of rolling of 2 dice is as below,

S = {(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)}

n(S) = 36

Let A = sum of numbers is 7 = { (1, 6)(2, 5)(3, 4) (4, 3) (5, 2) (6, 1)}

n(A) = 6

P (Sum of numbers is 7) = n(A) / n(S)

= 6/36 = 1/6

Therefore, the probability of rolling two dice and getting a sum of 7 is 1/6.

What is the probability of rolling two dice and getting a sum of 7

Summary:

The probability of rolling two dice and getting a sum of 7 is 1/6.

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Concept Used:

P(A) = Favorable outcomes/Total number of outcomes

Calculations:

Total number of possible outcomes = 6 × 6 = 36

Favorable outcomes = (1, 6) (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)

⇒ P(A) = 6/36 = 1/6

∴ The probability of getting sum as 7 when two dice are thrown is 1/6.

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Solution : The outcomes of the rolling of a pair of dice can be more readily understood by assigning colors to the dice (e.g ., one red , one green ). An outcome of throwing aa pair of dice can be represented by an ordered pair , where the first element is the side of the red die fecing up, and the second is the side of the green die fecing up . Thus , (32) signifies a 3 on the red die and a 2 on the green, while (23) signifies 2 on the red 3 on the green . Since there are ltbr. six feces on each die , there are ` 6xx6 = 36` possible outcomes in the same space . the outcomes that have a sum of 7 are (61). (16), (52) , (25) , (43) and (34) . Therefore , the probability of getting a sum of 7 is `(6)/(36) = (1)/(6)` Probability questions can also be asked about two events A and B . Questions on the Math Leval 2 Test cover the following three ways of combining two events `*P(A cupB)` , the probability of either A or B occurring . where ` A cup B ` is called the disjunction of A and B ` * (PA|B)` , the probability of A occurring , givne that B has occurred . This is called conditional Probability ` * P(A nn B)` , the probabilty of both A and B occurring , where ` A nn B ` is called the conjunction of A and B If two event have no outcomes in common , they are called mutually exclusive , and `P(A uu B) = ` P(A) + P(B) . If two event no outcomes in common , these outcomes would be double counted , resulting i the more general formaula ` P(AuuB)= P(A) + P(A) - P(AnnB) ` . Note that A and B are mutually exclusive if and only if ` P(A nn B ) = 0 ` .

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