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Choose the correct alternative: If A and B are any two events, then the probability that exactly one of them occur is - Mathematics

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प्रश्न

Choose the correct alternative:

If A and B are any two events, then the probability that exactly one of them occur is

पर्याय

  • `"P"("A" ∪ bar"B") + P(bar"A" ∪ "B")`

  • `"P"("A" ∩ bar"B") + P(bar"A" ∩ "B")

  • P(A) + P(B) – P(A ∩ B)

  • P(A) + P(B) + 2P(A ∩ B)

MCQ
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उत्तर

`"P"("A" ∩ bar"B") + P(bar"A" ∩ "B")

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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 4 | पृष्ठ २६५

संबंधित प्रश्‍न

A fair coin is tossed five times. Find the probability that it shows exactly three times head.


A die is thrown three times. Events A and B are defined as below:
A : 5 on the first and 6 on the second throw.
B: 3 or 4 on the third throw.

Find the probability of B, given that A has already occurred.


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 ?


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).

Two coins are tossed once, where 

E: no tail appears, F: no head appears


A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.


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?


An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement, What is the probability that at least one ball is black?


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


Can two events be mutually exclusive and independent simultaneously?


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


If P(A ∩ B) = `7/10` and P(B) = `17/20`, then P(A|B) equals ______.


A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag and 2 balls are drawn from the second bag, then find the probability that all three balls are of the same colour.


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 ______.


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 ______.


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


Students of under graduation submitted a case study on “Understanding the Probability of Left-Handedness in Children Based on Parental Handedness”. Following Recent studies suggest that roughly 12% of the world population is left-handed. Depending on the parents’ handedness, the chances of having a left-handed child are as follows:

Scenario A: Both parents are left-handed, with a 24% chance of the child being left-handed.

Scenario B: The fathers is right-handed and the mothers left-handed, with a 22% chance of child being left-handed.

Scenario C: The fathers left-handed and the mother is right-handed, with a 17% chance of child being left-handed.

Scenario D: Both parents are right-handed, with a 9% chance of having a left-handed child.

Assuming that scenarios A, B, C and D are equally likely and L denotes the event that the child is left-handed, answer the following questions.

  1. What is the overall probability that a randomly selected child is left-handed?
  2. Given that exactly one parent is left-handed, what is the probability that a randomly selected child is left-handed?
  3. If a child is left-handed, what is the probability that both parents are left-handed?

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


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