A dice is thrown once. The probability of getting a number which
(i) A prime number
(ii) A number lying between 2 and 6.
Last updated date: 19th Mar 2023
•
Total views: 304.8k
•
Views today: 6.82k
Answer
304.8k+ views
Hint: To solve the question, we have to calculate the number of possible outcomes at the given conditions. To calculate probability divide the obtained number of outcomes to the total number of outcomes obtained when a dice is thrown.
Complete step-by-step answer:
The number of possible outcomes when a dice is thrown = 6
Since, a dice is a cube which is number 1, 2, 3, 4, 5, 6 on its 6 faces.
2, 3, 5 are the prime numbers among the numbers obtained when a dice is thrown.
Thus, the number of outcomes of getting a prime number when a dice is thrown = 3.
The probability of getting a prime number when a dice is thrown = Ratio of the number of outcomes of number between 2 and 6 prime number when a dice is thrown to the number of possible outcomes when a dice is thrown
\[=\dfrac{3}{6}\]
\[=\dfrac{1}{2}\]
\[\therefore \] The probability of getting a prime number when a dice is thrown \[=\dfrac{1}{2}=0.5\]
3,4,5 are the numbers between 2 and 6 which can be obtained when a dice is thrown.
Thus, the number of outcomes of getting a number between 2 and 6 when a dice is thrown = 3.
The probability of getting a number between 2 and 6 when a dice is thrown = Ratio of the number of outcomes of getting a number between 2 and 6 when a dice is thrown to the number of possible outcomes when a dice is thrown
\[=\dfrac{3}{6}\]
\[=\dfrac{1}{2}\]
\[\therefore \] The probability of getting a number between 2 and 6 when a dice is thrown \[=\dfrac{1}{2}=0.5\]
Note: The alternative quick method is that the answer for both the given cases will be the same since the number of required outcomes are equal.
Complete step-by-step answer:
The number of possible outcomes when a dice is thrown = 6
Since, a dice is a cube which is number 1, 2, 3, 4, 5, 6 on its 6 faces.
2, 3, 5 are the prime numbers among the numbers obtained when a dice is thrown.
Thus, the number of outcomes of getting a prime number when a dice is thrown = 3.
The probability of getting a prime number when a dice is thrown = Ratio of the number of outcomes of number between 2 and 6 prime number when a dice is thrown to the number of possible outcomes when a dice is thrown
\[=\dfrac{3}{6}\]
\[=\dfrac{1}{2}\]
\[\therefore \] The probability of getting a prime number when a dice is thrown \[=\dfrac{1}{2}=0.5\]
3,4,5 are the numbers between 2 and 6 which can be obtained when a dice is thrown.
Thus, the number of outcomes of getting a number between 2 and 6 when a dice is thrown = 3.
The probability of getting a number between 2 and 6 when a dice is thrown = Ratio of the number of outcomes of getting a number between 2 and 6 when a dice is thrown to the number of possible outcomes when a dice is thrown
\[=\dfrac{3}{6}\]
\[=\dfrac{1}{2}\]
\[\therefore \] The probability of getting a number between 2 and 6 when a dice is thrown \[=\dfrac{1}{2}=0.5\]
Note: The alternative quick method is that the answer for both the given cases will be the same since the number of required outcomes are equal.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
