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Choose the correct alternative: If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is - Mathematics

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प्रश्न

Choose the correct alternative:

If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is

पर्याय

  • `5/13`

  • `1/13`

  • `4/13`

  • `7/13`

MCQ
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उत्तर

`5/13`

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Introduction to probability theory - Exercise 12.5 [पृष्ठ २६७]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 12 Introduction to probability theory
Exercise 12.5 | Q 16 | पृष्ठ २६७

संबंधित प्रश्‍न

40% students of a college reside in hostel and the remaining reside outside. At the end of the year, 50% of the hostelers got A grade while from outside students, only 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to have gotten A grade. What is the probability that the selected student was a hosteler ?


Suppose that 80% of all families own a television set. If 5 families are interviewed at  random, find the probability that
a. three families own a television set.
b. at least two families own a television set.


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 coin is tossed three times, where 

E: at least two heads, F: at most two heads


Determine P(E|F).

Two coins are tossed once, where 

E: tail appears on one coin, F: one coin shows head


A black and a red dice are rolled. 

Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.


If P(A) = `1/2`,  P(B) = 0, then P(A|B) is ______.


A die is tossed thrice. Find the probability of getting an odd number at least once.


The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If the oil had to be changed, what is the probability that a new oil filter is needed?


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


Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.


Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events


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


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


Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?


In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______ 


If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `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)

Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.


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