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तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता 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

पर्याय

  • 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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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Introduction to probability theory - Exercise 12.5 [पृष्ठ २६५]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 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

  1. P(A ∩ B)
  2. P(A|B)
  3. P(A ∪ B)

Determine P(E|F).

A die is thrown three times,

E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses


A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|G) and P (G|E)


Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that

  1. both balls are red.
  2. first ball is black and second is red.
  3. one of them is black and other is red.

If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?


Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white ·and four black balls. A dice having three red, two yellow and one green face, is thrown to select the box. If red face turns up, we pick up the box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the ball is drawn is white, what is the probability that the dice had turned up with a red face?


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


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 one white and one black


Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(B/A) = 0.5


A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays


Three machines E1, E2, E3 in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.


Let A and B be two events. If P(A) = 0.2, P(B) = 0.4, P(A ∪ B) = 0.6, then P(A|B) is equal to ______.


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 ______.


For a biased dice, the probability for the different faces to turn up are

Face 1 2 3 4 5 6
P 0.10 0.32 0.21 0.15 0.05 0.17

The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is ______.


It is given that the events A and B are such that P(A) = `1/4, P(A/B) = 1/2` and `P(B/A) = 2/3`, then P(B) is equal to ______. 


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)

Three friends go to a restaurant to have pizza. They decide who will pay for the pizza by tossing a coin. It is decided that each one of them will toss a coin and if one person gets a different result (heads or tails) than the other two, that person would pay. If all three get the same result (all heads or all tails), they will toss again until they get a different result.

  1. What is the probability that all three friends will get the same result (all heads or all tails) in one round of tossing?
  2. What is the probability that they will get a different result in one round of tossing?
  3. What is the probability that they will need exactly four rounds of tossing to determine who would pay?

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