Physics Exam > Physics Questions > In a colony all families have at least one ch...
Start Learning for Free
In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________
Correct answer is '0.3 to 0.4'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
In a colony all families have at least one child. The probability that...
The probability that a randomly chosen family from this colony has exactly k children is given by (0.5)^k, where k = 1, 2, K.
To find the probability that such a family consists of at least one male child and at least one female child, we need to consider two cases:
Case 1: Only one child in the family
Since a family must have at least one child, the probability of having exactly one child is 1. In this case, the probability of having both a male and a female child is 0.5 * 0.5 = 0.25.
Case 2: More than one child in the family
In this case, we need to find the probability of having at least one male child and at least one female child among the k children.
To do this, we can find the probability of the complementary event, which is having either all male or all female children.
The probability of having all male children is (0.5)^k, and the probability of having all female children is also (0.5)^k.
So, the probability of having either all male or all female children is 2 * (0.5)^k.
Therefore, the probability of having at least one male and at least one female child among the k children is 1 - 2 * (0.5)^k.
To find the overall probability, we need to consider both cases.
The probability of having exactly one child is 1, and the probability of having both a male and a female child is 0.25.
So, the overall probability is 1 * 0.25 + (1 - 0.25) * (1 - 2 * (0.5)^k).
Simplifying this expression, we get 0.25 + (1 - 0.25) * (1 - 2 * (0.5)^k) = 0.25 + 0.75 * (1 - 2 * (0.5)^k).
Since the given answer is '0.3 to 0.4', we can infer that the value of 0.25 + 0.75 * (1 - 2 * (0.5)^k) lies within this range for k = 1, 2, K.
To find the probability that such a family consists of at least one male child and at least one female child, we need to consider two cases:
Case 1: Only one child in the family
Since a family must have at least one child, the probability of having exactly one child is 1. In this case, the probability of having both a male and a female child is 0.5 * 0.5 = 0.25.
Case 2: More than one child in the family
In this case, we need to find the probability of having at least one male child and at least one female child among the k children.
To do this, we can find the probability of the complementary event, which is having either all male or all female children.
The probability of having all male children is (0.5)^k, and the probability of having all female children is also (0.5)^k.
So, the probability of having either all male or all female children is 2 * (0.5)^k.
Therefore, the probability of having at least one male and at least one female child among the k children is 1 - 2 * (0.5)^k.
To find the overall probability, we need to consider both cases.
The probability of having exactly one child is 1, and the probability of having both a male and a female child is 0.25.
So, the overall probability is 1 * 0.25 + (1 - 0.25) * (1 - 2 * (0.5)^k).
Simplifying this expression, we get 0.25 + (1 - 0.25) * (1 - 2 * (0.5)^k) = 0.25 + 0.75 * (1 - 2 * (0.5)^k).
Since the given answer is '0.3 to 0.4', we can infer that the value of 0.25 + 0.75 * (1 - 2 * (0.5)^k) lies within this range for k = 1, 2, K.
Free Test
FREE
| Start Free Test |
Community Answer
In a colony all families have at least one child. The probability that...
0.25
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer?
Question Description
In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer?.
In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer?.
Solutions for In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer?, a detailed solution for In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? has been provided alongside types of In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a colony all families have at least one child. The probability that a randomly chosen family from this colony has exactly k children is (0.5)k ; k = 1, 2,K . A child is either a male or a female with equal probability. The probability that such a family consists of at least one male child and at least one female child is _________ Correct answer is '0.3 to 0.4'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup