Question

the probability of guessing the correct answer to a certain question is x/3. If the probability of not guessing the correct answer is x/5. find the value of x.​

Answer 1

★Given:-

• The probability of guessing the correct answer to a certain question is x/3.
• The probability of not guessing the correct answer is x/5.

★To find:-

• Value of x.

★Solution:-

We know,

✦Probability of an event is always is greater than or equal to zero, and less than or equal to one.

✦The sum of the probabilities of all outcomes must be equal to 1.  

Therefore,

The probability of guessing the correct answer to a certain question added to the probability of not guessing the correct answer should be equal to 1.

That is,

➺x/3 + x/5 = 1

➺(5x + 3x)/15 = 1

➺8x/15 = 1

➺8x = 15

➺x = 15/8

Hence,the value of x is 15/8.

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Points to remember:-

✦Probability:

• A branch of mathematics that deals with the occurrence of a random event.
• Probability is a number that can be assigned to outcomes and events.

✦If two events have no outcomes in common,the probability that one or the other occurs is the sum of their individual probabilities.

✦The probability that an event does not occur is 1 - the probability that the event does occur.

✦An impossible event, or an event that never occurs, has a probability of  0

✦An event that always occurs has a probability of  1.

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Answer 2

$\red{\sf{\star\;Appropriate\; Question :-}}$

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• the probability of guessing the correct answer to a certain question is x/3. If the probability of not guessing the correct answer is x/5. find the value of x.

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$\purple{\sf{\star\;To\; Find :—}}$ value of X

⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\green{\sf{\star\;Required \;Solution:—}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Probability Of Guessing The Correct Answer = x/3

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Probability of Not Guessing The Wrong Answer = 1 - x/3 --- to test this 

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$\blue{\sf{\star\;Step-\; by\; -Explanation:—}}$

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➥ x / 5 = 1 -x/3                                                          ⠀ take example 

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➥x /5 = (3 - x) / 3                                                        ⠀of 1 coin tossed

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➥ 3x = 5(3 - x)                                                       ⠀in air and let assume

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➥3x = 15 - 5x                                                            ⠀ P of getting tail is 

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➥3x + 5x = 15                                                        ⠀ 25% so P of getting

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➥ 8x = 15                                                                   ⠀ ⠀Head is 1 - 25% 

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➥ x = 15/8                                                                  ⠀ ⠀⠀⠀which is 75%

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\pink{\sf{\star\;Value \;Of\; X \;is \;15/8}}$ ✔

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