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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

विकल्प

  • `5/13`

  • `1/13`

  • `4/13`

  • `7/13`

MCQ
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उत्तर

`5/13`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Introduction to probability theory - Exercise 12.5 [पृष्ठ २६७]

APPEARS IN

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

संबंधित प्रश्न

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls? Given that

  1. the youngest is a girl.
  2. at least one is a girl.

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


Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`


Determine P(E|F).

A coin is tossed three times, where

E: head on third toss, F: heads on first two tosses


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)


An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple-choice question?


A card is drawn from a well-shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both? 


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?


Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes.


Can two events be mutually exclusive and independent simultaneously?


If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)


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(B/A) = 0.5


Choose the correct alternative:

A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are `3/4, 1/2, 5/8`. The probability that the target is hit by A or B but not by C is


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

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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