मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता ११

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive

Advertisements
Advertisements

प्रश्न

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive

बेरीज
Advertisements

उत्तर

P(A) = 0.4

P(A ∪ B) = 0.7

When A and B are mutually exclusive

P(A ∪ B) = P(A) P(B)

(i.e.,) 0.7 = 0.4 + P(B)

0.7 – 0.4 = P(B)

(i.e.,) P(B) = 0.3

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Introduction to probability theory - Exercise 12.3 [पृष्ठ २५९]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 12 Introduction to probability theory
Exercise 12.3 | Q 10. (i) | पृष्ठ २५९

संबंधित प्रश्‍न

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


If `P(A) = 6/11, P(B) = 5/11 "and"  P(A ∪ B) = 7/11` find

  1. P(A ∩ B)
  2. P(A|B)
  3. P(B|A)

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?


 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 dice are thrown simultaneously, If at least one of the dice show a number 5, what is the probability that sum of the numbers on two dice is 9?


In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in exactly one subject?


From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when the first card drawn is replaced in the pack


If for two events A and B, P(A) = `3/4`, P(B) = `2/5`  and A ∪ B = S (sample space), find the conditional probability P(A/B)


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 the problem is solved?


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 black


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


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


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.


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


Which statement is the multiplication rule for two events A and B?


If A and B are any two events of S and \[P(F)\neq 0\], which formula is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×