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There are two boxes marked A and B. Box A contains 4 red and 3 white balls, and Box B contains 3 red and 4 white balls. A box is selected at random and a ball is taken from it. Probability that the ball is white is (a) $\frac{1}{2}$ (b) $\frac{12}{49}$ (c) $\frac{37}{49}$ (d) $\frac{1}{4}$

Name: Problem 57, Chapter 4: IIT JEE Super Course in Mathematics ALGEBRA II
Uploaded: 2021-06-07T20:41:18-08:00
Duration: 3 min 43 s
Channel: Anas Venkitta
Description: There are two boxes marked A and B. Box A contains 4 red and 3 white balls, and Box B contains 3 red and 4 white balls. A box is selected at random and a ball is taken from it. Probability that the ball is white is (a) (1)/(2) (b) (12)/(49) (c) (37)/(49) (d) (1)/(4)

   There are two boxes marked A and B. Box A contains 4 red and 3 white balls, and Box B contains 3 red and 4 white balls. A box is selected at random and a ball is taken from it. Probability that the ball is white is
(a) $\frac{1}{2}$
(b) $\frac{12}{49}$
(c) $\frac{37}{49}$
(d) $\frac{1}{4}$

IIT JEE Super Course in Mathematics ALGEBRA II

Trishna Knowledge… 2011 Edition

Chapter 4, Problem 57

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Solved by Expert Anas Venkitta

06/07/2021

Step 1

Box A contains 4 red and 3 white balls, and Box B contains 3 red and 4 white balls. We are asked to find the probability that a ball drawn at random from a randomly chosen box is white. Show more…

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There are two boxes marked A and B. Box A contains 4 red and 3 white balls, and Box B contains 3 red and 4 white balls. A box is selected at random and a ball is taken from it. Probability that the ball is white is (a) $\frac{1}{2}$ (b) $\frac{12}{49}$ (c) $\frac{37}{49}$ (d) $\frac{1}{4}$

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Key Concepts

Conditional Probability

Conditional probability is the concept of finding the likelihood of an event occurring, given that another event has already occurred. In the context of drawing a ball from a box, it involves determining the probability of selecting a white ball given a particular box has been chosen.

Law of Total Probability

The law of total probability is a method used to compute the overall probability of an event by considering all different scenarios that could lead to that event. It involves summing the products of the conditional probabilities and the probabilities of the associated conditions (such as which box was selected).

Uniform Random Selection

Uniform random selection refers to the process where each option within a set (for example, the two boxes) is equally likely to be chosen. This assumption is crucial in problems where the initial choice influences the subsequent probability calculations.

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