Question

A pair of dice thrown if \[5\] appears on at least one of the dice, then probability that the sum is \[10\] or greater is
A. \[\dfrac{11}{36}\]
B. \[\dfrac{2}{9}\]
C. \[\dfrac{3}{11}\]
D. \[\dfrac{1}{12}\]

Answer 1

Hint: In these types of questions firstly we have to find out the sample space that tells us about the total number of outcomes and after that we have to identify the event and we have to find out the favorable outcomes. After that we have to find the ratio оf the number оf fаvоrаble events to the total number of possible outcomes.

Complete step by step answer:
Probability is defined аs the роssibility оf an event to оссur. For example: if we toss a coin then there are only two possibilities: either head will occur or tail. The probability of occurrence of head is half and the probability of occurrence of tail is half.
The formula for Probability is given аs the ratio of the number оf fаvоrаble events to the total number of possible outcomes. There are three types of probability:
Theoretical Probability
Experimental Probability
Axiomatic Probability
In theoretical Probability, it depends on all the possible chances of something to happen.
In experimental probability, it depends on the observations of the experiment. It is calculated as the number of all the possible outcomes to the number of trials.
In axiomatic probability, it tells the chances of the occurrence or non-occurrence of the event.
Now according to the given question:
Let there be two dice \[A\] and\[B\]. Both the dice are distinct.
So, the numbers on each of the dice can have values as: \[1,2,3,4,5\]and\[6\].
Let the ordered pair \[(x,y)\] where \[x\] denotes the numbers appearing on the dice \[A\]and y denotes all the numbers appearing on the dice\[B\].
As the given condition says that at least one of the dice has number \[5\] on it and the sum of numbers on both the dice is \[10\] or greater than it i.e., \[x+y\ge 10\]
So the sample space is given as:
\[S'=(5,1),(5,2)(5,3),(5,4),(5,5),(5,6),(1,5),(2,5),(3,5),(4,5),(6,5)\]
As the sample space has \[11\] elements.
So, total number of outcomes \[n(S')=11\]
As, event says that the sum of both the numbers on dice should be \[\ge 10\].
So, even can be defined as:
\[E=(5,5),(5,6),(6,5)\]
Clearly, \[n(E)=3\]
So, the probability that the sum is \[10\] or greater than it when at least one of the dice has number \[5\]
\[P(E)=\dfrac{n(E)}{\begin{align}
  & n(S') \\
 & \\
\end{align}}\]
\[P(E)=\dfrac{3}{11}\]

So, the correct answer is “Option C”.

Note: Uses of probability in our day to day life:
Used to predict the weather changes.
Used in games such as poker, blackjack etc to know the probability of the person to win.
Political analysts use probability to predict the outcomes of the election’s result.
Winning or losing the lottery is also interesting.