Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A die is loaded in such a way that the probability of getting a 6 is twice the probability of getting any other number. What is the probability of getting a prime number when the die is r

A die is loaded in such a way that the probability of getting a 6 is twice the probability of getting any other number. What is the probability of getting a prime number when the die is rolled?

Option: 1

\frac{1}{2}


Option: 2

\frac{1}{4}


Option: 3

\frac{1}{5}


Option: 4

\frac{1}{8}

 


Answers (1)

best_answer

Let P(A) be the probability of getting a 6 and P(B) be the probability of getting any other number. 

From the given information, we know that P(A) = 2P(B). 

Let P(C) be the probability of getting a prime number when the die is rolled. 

We can use the theorem of total probability to find P(C). 

The events that can occur when the die is rolled are: getting a 6 and getting any other number. So,

{P(C)=P(C/A)\times P(A)+P(C/B)\times P(B)}

Since the die is loaded in such a way that the probability of getting a 6 is twice the probability of getting any other number, we have: 

P(A) = 2P(B) 

Therefore,

{P(C)=2P(C/A)\times P(B)+P(C/B)\times P(B)}

Now, we need to find P(C | A) and P(C | B).

When the die shows a 6, we cannot get a prime number. 

So, P(C | A) = 0. 

When the die shows a number other than 6, the prime numbers that can be obtained are 2, 3, and 5. 

So,

{P(C/B)=\frac{3}{5}}

Substituting these values, we get:

{P(C)=0+\ \frac{3}{5}P(B)}

We know that P(A) + P(B) = 1 and P(A) = 2P(B).

\Rightarrow {P(B)=\frac{1}{3}} \ \text{and} \ {P(A)=\frac{2}{3}}

Substituting these values, we get:

\\{P(C)=\frac{3}{5}\times \frac{1}{3}}\\ \\\Rightarrow {P(C)=\frac{1}{5}}

Therefore, the probability of getting a prime number when the die is rolled is {\frac{1}{5}}.

Posted by

manish painkra

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

NTA finds errors in JEE Main 2025 photos; asks to upload correct images by January 17
anam-khan

JEE Main 2025 Live: NTA finds errors in images, starts application correction; photo requirements
anam-khan

NTA Exams 2025 Live: NEET UG date, registration form soon at neet.nta.nic.in; UGC NET revised schedule out

Latest Question