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If three dice are thrown, then the probability that they show the numbers in A.P. is
- a)1/12
- b)7/36
- c)1/36
- d)1/18
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If three dice are thrown, then the probability that they show the numb...
A.P. with common diff one are =4=(123)(234)(345)(456)
A.P. with common diff 2 are =2=(135)(246)
A.P. with common diff 0 are =6
⇒P=2+4+6/216=1/18
A.P. with common diff 2 are =2=(135)(246)
A.P. with common diff 0 are =6
⇒P=2+4+6/216=1/18
Most Upvoted Answer
If three dice are thrown, then the probability that they show the numb...
Let's consider the numbers on the three dice as a, a + d, and a + 2d, where a is the first term and d is the common difference. We need to find the probability that these three numbers are in arithmetic progression (A.P.).
There are a total of 6^3 = 216 possible outcomes when three dice are thrown since each die has 6 possible outcomes.
To find the favorable outcomes, we need to consider the possible values of a and d that satisfy the condition of an A.P.
- Finding the possible values of a and d:
For a = 1, the possible values of d can be 1, 2, 3, 4, or 5.
For a = 2, the possible values of d can be 1, 2, 3, or 4.
For a = 3, the possible values of d can be 1, 2, or 3.
For a = 4, the possible values of d can be 1 or 2.
For a = 5, the only possible value of d is 1.
Therefore, there are a total of (5 + 4 + 3 + 2 + 1) + (4 + 3 + 2 + 1) + (3 + 2 + 1) + (2 + 1) + 1 = 35 possible combinations of a and d that form an A.P.
- Calculating the probability:
The probability of getting an A.P. is given by the ratio of favorable outcomes to total outcomes.
P(A.P.) = favorable outcomes / total outcomes
= 35 / 216
Simplifying the fraction, we get:
P(A.P.) = 5 / 36
Therefore, the correct answer is option D: 1/18.
There are a total of 6^3 = 216 possible outcomes when three dice are thrown since each die has 6 possible outcomes.
To find the favorable outcomes, we need to consider the possible values of a and d that satisfy the condition of an A.P.
- Finding the possible values of a and d:
For a = 1, the possible values of d can be 1, 2, 3, 4, or 5.
For a = 2, the possible values of d can be 1, 2, 3, or 4.
For a = 3, the possible values of d can be 1, 2, or 3.
For a = 4, the possible values of d can be 1 or 2.
For a = 5, the only possible value of d is 1.
Therefore, there are a total of (5 + 4 + 3 + 2 + 1) + (4 + 3 + 2 + 1) + (3 + 2 + 1) + (2 + 1) + 1 = 35 possible combinations of a and d that form an A.P.
- Calculating the probability:
The probability of getting an A.P. is given by the ratio of favorable outcomes to total outcomes.
P(A.P.) = favorable outcomes / total outcomes
= 35 / 216
Simplifying the fraction, we get:
P(A.P.) = 5 / 36
Therefore, the correct answer is option D: 1/18.
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If three dice are thrown, then the probability that they show the numbers in A.P. isa)1/12b)7/36c)1/36d)1/18Correct answer is option 'D'. Can you explain this answer?
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If three dice are thrown, then the probability that they show the numbers in A.P. isa)1/12b)7/36c)1/36d)1/18Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If three dice are thrown, then the probability that they show the numbers in A.P. isa)1/12b)7/36c)1/36d)1/18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If three dice are thrown, then the probability that they show the numbers in A.P. isa)1/12b)7/36c)1/36d)1/18Correct answer is option 'D'. Can you explain this answer?.
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