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Question: The chance of getting a doublet with \(2\) dice is A. \(\dfrac{2}{3}\) B. \(\dfrac{1}{6}\) C. ...

The chance of getting a doublet with 22 dice is
A. 23\dfrac{2}{3}
B. 16\dfrac{1}{6}
C. 56\dfrac{5}{6}
D. 536\dfrac{5}{{36}}

Explanation

Solution

Probability can be defined as the state of being probable and the extent to which something is likely to happen in the particular situations or the favourable outcomes. Probability of any given event is given by the ratio of the favourable outcomes with the total number of the outcomes. Here we will first find the total possible outcomes and then the outcomes of both the dice to be the same and then will find its probability accordingly.

Complete step by step answer:
Given that the two dice are thrown together.
Outcomes would be –

\Rightarrow (2,1)\;{\text{(2,2) (2,3) (2,4) (2,5) (2,6)}} \\\ \Rightarrow (3,1)\;{\text{(3,2) (3,3) (3,4) (3,5) (3,6)}} \\\ \Rightarrow (4,1)\;{\text{(4,2) (4,3) (4,4) (4,5) (4,6)}} \\\ \Rightarrow (5,1)\;{\text{(5,2) (5,3) (5,4) (5,5) (5,6)}} \\\ \Rightarrow (6,1)\;{\text{(6,2) (6,3) (6,4) (6,5) (6,6)}} \\\ $$ The total possible outcomes from the two thrown dices will be $ = 36$ ..... (A) In dice, doublet means the throw of a pair of dice in which the same number turns up in each of the dies. Favourable outcomes = $(1,1){\text{ (2,2) (3,3) (4,4) (5,5) (6,6) }}$ The total number of favourable outcomes $ = 6$ .... (B) By using the values of equations, A and B The probability that A wills – $P(A) = \dfrac{6}{{36}}$ Find the factors for the above terms for the above fraction – $P(A) = \dfrac{{6 \times 1}}{{6 \times 6}}$ Common factors from the numerator and the denominator in the above fraction cancel each other and therefore remove from the numerator and the denominator. $\therefore P(A) = \dfrac{1}{6}$ **Hence, option B is the correct answer.** **Note:** Probability always lies between the number zero and one. Be good in multiples and division and always remove common factors from the numerator and the denominator to get the simplified form. Read the question twice and understand the required probability, know the difference between the doublet, double and twice words.