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तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Choose the correct alternative: Let A and B be two events such that PABPABP(A∪B¯)=16,P(A∩B)=14 and PAP(A¯)=14. Then the events A and B are

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प्रश्न

Choose the correct alternative:

Let A and B be two events such that `"P"(bar ("A" ∪ "B")) = 1/6, "P"("A" ∩ "B") = 1/4` and `"P"(bar"A") = 1/4`. Then the events A and B are

विकल्प

  • Equally likely but not independent

  • Independent but not equally likely

  • Independent and equally likely

  • Mutually inclusive and dependent

MCQ
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उत्तर

Independent but not equally likely

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Introduction to probability theory - Exercise 12.5 [पृष्ठ २६५]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 12 Introduction to probability theory
Exercise 12.5 | Q 5 | पृष्ठ २६५

संबंधित प्रश्न

The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive


Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).


If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find  P(A ∪ B)


Determine P(E|F).

A coin is tossed three times, where

E: at most two tails, F: at least one tail


 Two balls are drawn from an urn containing 3 white, 5 red and 2 black balls, one by one without replacement. What is the probability that at least one ball is red?


In a college, 70% of students pass in Physics, 75% pass in Mathematics and 10% of students fail in both. One student is chosen at random. What is the probability that:
(i) He passes in Physics and Mathematics?
(ii) He passes in Mathematics given that he passes in Physics.
(iii) He passes in Physics given that he passes in Mathematics.


Two cards are drawn one after the other from a pack of 52 cards without replacement. What is the probability that both the cards drawn are face cards?


If A and B are two events such that P(A ∪ B) = 0.7, P(A ∩ B) = 0.2, and P(B) = 0.5, then show that A and B are independent


A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that exactly one of them will solve it?


One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are white


A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______


Find the probability that in 10 throws of a fair die a score which is a multiple of 3 will be obtained in at least 8 of the throws.


If P(A) = `4/5`, and P(A ∩ B) = `7/10`, then P(B|A) is equal to ______.


A bag contains 6 red and 5 blue balls and another bag contains 5 red and 8 blue balls. A ball is drawn from the first bag and without noticing its colour is placed in the second bag. If a ball is drawn from the second bag, then find the probability that the drawn ball is red in colour.


A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.


If A and B are two events such that P(A) = `1/3`, P(B) = `1/5` and P(A ∪ B) = `1/2`, then P(A|B') + P(B|A') is equal to ______.


Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is ______.


If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is ______.


Read the following passage:

Recent studies suggest the roughly 12% of the world population is left-handed.

Depending upon the parents, the chances of having a left-handed child are as follows:

A :  When both father and mother are left-handed:
Chances of left-handed child is 24%.
B :  When father is right-handed and mother is left-handed:
Chances of left-handed child is 22%.
C :  When father is left-handed and mother is right-handed:
Chances of left-handed child is 17%.
D :  When both father and mother are right-handed:
Chances of left-handed child is 9%.

Assuming that P(A) = P(B) = P(C) = P(D) = `1/4` and L denotes the event that child is left-handed.

Based on the above information, answer the following questions:

  1. Find `P(L/C)` (1)
  2. Find `P(overlineL/A)` (1)
  3. (a) Find `P(A/L)` (2)
    OR
    (b) Find the probability that a randomly selected child is left-handed given that exactly one of the parents is left-handed. (2)

If P(B) = `3/5`, P(A | B) = `1/2` and P(A ∪ B) = `4/5`, then P(A ∪ B) + P(A' ∪ B) =


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