Question

Question:-->
$\small\purple{\sf{Two \: fair \: dice \: are \: rolled. What \: is \: the}} \\ \small{\sf{ \red{probability} \purple {\: that \: their \: sum \: is \: greater \: than \: 4}}}$
PROBABILITY ​

Answer 1

The set of possible outcomes when we roll a die are {1, 2, 3, 4, 5, 6}

So, when we roll two dice there are 6 × 6 = 36 possibilities.

When we roll two dice, the possibility of getting number 4 is (1, 3), (2, 2), and (3, 1).

So,

The number of favorable outcomes = 3

Total number of possibilities = 36

Probability = The number of favorable outcomes / Total number of possibilities = 3 / 36 = 1/12.

Thus, 1/12 is the probability of rolling two dice and getting a sum of 4.

please give me brain list and thanks

Answer 2

$\large\underline{\sf{Solution-}}$

As it is given that two fair dice are rolled. So, possible outcomes when 2 dices are thrown are as under

$\begin{gathered}\begin{gathered}\bf\: S = \begin{cases} &\sf{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),} \\ &\sf{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),}\\ &\sf{(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),}\\ &\sf{(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),}\\ &\sf{(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),}\\ &\sf{(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)} \end{cases}\end{gathered}\end{gathered}$

$\rm\implies \:n(S) = 36$

Now, we have to find the probability of getting sum of two numbers appear on dice is greater than 4.

E = { getting sum of two numbers appear is greater than 4}

So, favourable outcomes are

$\begin{gathered}\begin{gathered}\bf\: E = \begin{cases} &\sf{(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),} \\ &\sf{(2,6),(3,2),(3,3),(3,4),(3,5),(3,6),}\\ &\sf{(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),}\\ &\sf{(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),}\\ &\sf{(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)} \end{cases}\end{gathered}\end{gathered}$

$\rm\implies \:n(E) = 30$

Now, we know, Probability of happening of the event E is evaluated as

$\rm \: P(E) = \dfrac{n(E)}{n(S)}$

$\rm \: P(E) = \dfrac{30}{36}$

$\rm\implies \:\boxed{ \rm{ \:\rm \: P(E) = \dfrac{5}{6} \: \: }}$

$\rule{190pt}{2pt}$

Additional information :-

1. The sample space is the collection of all possible outcomes associated with the random experiment.

2. The probability of an event belongs to [0, 1]

3. The probability of sure event is 1.

4. The probability of impossible event is 0.

5. P(E) + P(not E) = 1