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Question 4 - Miscellaneous - Chapter 13 Class 12 Probability
Last updated at April 16, 2024 by Teachoo
Question 4 An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes. Let X: Number of successes Since we are talking about success and failure It is a Bernoulli trial So, X has a binomial distribution Here, n = number of trials = 6 p = Probability of success q = Probability of failure = 1 – p Let X: Number of successes Since we are talking about success and failure It is a Bernoulli trial So, X has a binomial distribution Here, n = number of trials = 6 p = Probability of success q = Probability of failure = 1 – p Let X: Number of successes Since we are talking about success and failure It is a Bernoulli trial So, X has a binomial distribution Here, n = number of trials = 6 p = Probability of success q = Probability of failure = 1 – p We need to probability that there will be at least 4 successes i.e. P(X ≥ 4) P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = 6C4(2/3)^4 (1/3)^(6−4)+"6C5" (2/3)^5 (1/3)^(6−5)+"6C6" (2/3)^6 (1/3)^(6−6) = 6C4(2/3)^4 (1/3)^2+"6C5" (2/3)^5 (1/3)^1+"6C6" (2/3)^6 (1/3)^0 = 15 × (2/3)^4 (1/3)^2+"6" (2/3)^5 (1/3)^1+"1" (2/3)^6 × 1 = (2/3)^4 ("15 × " (1/3)^2+"6" (2/3)(1/3)+(2/3)^2 ) = (2/3)^4 (15/9+12/9+4/9) = 𝟑𝟏/𝟗 (𝟐/𝟑)^𝟒
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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An experiment succeeds thrice as often as it fails. Find the probability that in the next live trials, there will be at least 3 successes.
Let the probability of success be p and that of failure be q. therefore, p=3q. since p+q=1 so, 3 q + q = 1 ⇒ q = 1 4 , p = 3 4 ∴ p ( a t l e a s t 3 s u c c e s s e s ) = p ( r ≥ 3 ) = p ( 3 ) + p ( 4 ) + p ( 5 ) using p ( r ) = n c r p 4 q n − r , where n=5 i.e., p ( r ≥ 3 ) = 5 c 3 ( 3 4 ) 3 ( 1 4 ) 5 − 3 + 5 c 4 ( 3 4 ) 4 ( 1 4 ) 5 − 4 + 5 c 5 ( 3 4 ) 5 ( 1 4 ) 5 − 5 ⇒ = 10 ( 27 1024 ) + 5 ( 81 1024 ) + 1 ( 243 1024 ) so, required probability = 918 1024 = 459 512 ..
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An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes.
An experiment succeeds twice as often as it fails. So, the probability of success is and the probability of failure is . In the next 5 tr ials , the experiment needs to succeed in 4 out of the 5 trials.
An experiment succeeds twice as often as it fails. Find the probability that in 4 trails there will be at least three success. Login. Study Materials. ... An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is. Q.
9. An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes. Solution: Given that probability of failure = x. And, the probability of success = 2x. ∴ x + 2x = 1. 3x = 1. X = 1/3. 2x = 2/3. Assume p = 1/3 and q = 2/3. Also, X be the random variable that represents ...
An experiment succeeds twice as often as it fails. This means out of x number of trials if the experiment fails y times then it gets success 2y times where $ y+2y=x\Rightarrow x=3y $ . From this we find the probability of the experiment succeeding where we denote that event as event A. So, $ p\left( A \right)=\dfrac{2y}{3y}=\dfrac{2}{3} $ .
An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success(1) 4/27(2) 8/27(3) 16/27(4) 24/...
Question From - NCERT Maths Class 12 Chapter 13 MISCELLANEOUS EXERCISE Question - 9 PROBABILITY CBSE, RBSE, UP, MP, BIHAR BOARDQUESTION TEXT:-An experiment s...
An experiment succeeds twice as often as it fails. Find the chance that in the next six trials, there shall be at least four successes.(a) $\\dfrac{233}{729}$(b) $\\dfrac{64}{729}$(c) $\\dfrac{496}{729}$(d) $\\dfrac{432}{729}$. ... There is an experiment which succeeds twice as often as it fails. This means that the probability of success of ...
An experiment succeeds twice as often as it fails. Find the probability that in the next six trails, there will be at least 4 successes.. Ans: Hint: Use binomial distribution.Let success and failure probabilities are p, q respectively.
Transcript. Question 4 An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes. Let X: Number of successes Since we are talking about success and failure It is a Bernoulli trial So, X has a binomial distribution Here, n = number of trials = 6 p = Probability of ...
An experiment succeeds twice as often as it fails. The probability of at least five successes in the six trials of ... 729 (C) 240/729 (D) 256/729 ... An experiment succeeds twice as often as it fails. Find the probability that in the next six trails there will be at least 4 successes. asked May 2, 2018 in Mathematics by Nisa (60.9k points)
An experiment succeeds twice as often as it fails. Find the chance that in the next six trials, there shall be at least four successes. ... View Solution. Q5. An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is.
"An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes."jee mains 2020, jee ...
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will at least 4 successes.
An experiment succeeds twice as often as it fails. Find the probability that in next 6 trials, there will be more than 3 successes
An experiment succeeds twice as often as it fails. Find the probability that in 4 trails there will be at least three success A. \[\dfrac{4}{{27}}\]
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials there will be atleast 4 successes. Login. Study Materials. ... An experiment succeeds twice as often as it fails. Find the chance that in the next six trials, there shall be at least four successes.
Final answer: The probability of getting four successes in the next five trials is 80/243.. Explanation: To find the probability of getting four successes in the next five trials, we can use the binomial probability formula.In this case, since the experiment succeeds twice as often as it fails, the probability of success (p) is 2/3, and the probability of failure (q) is 1/3.
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes.📲PW App Link - https:...
An experiment succeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes.
Given that an experiment succeeds twice as often as it fails, this implies the probability of success (p) is twice the probability of failure (q). Since p + q = 1, we can deduce that p = 2q and hence p = 2/3 and q = 1/3. In a series of six trials, we want to find the probability of at least 4 successes (4, 5, or 6 successes).
An experiment succeeds twice as often as it fails. The probability of at least 1 successes in the six trials of this experiment is:
An experiment succeeds thrice as often as it fails. Find the probability that in the next live trials, there will be at least 3 successes. Login. Study Materials. ... An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is.