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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Baye’s theorem

Grade: 9-a Lesson: S3-L7

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	A bag I contains 4 white and 6 black balls while another Bag II contains 4 white and 3 black balls. One ball is drawn at random from one of the bags, and it is found to be black. Find the probability that it was drawn from Bag I by using bayes theorem.
2	Step	E1 be the event of choosing bag I, E2 the event of choosing bag II, and A be the event of drawing a black ball.
3	Step	probability of two events are equal	P(E1) = P(E2) = \$\frac(1)(2)\$
4	Step	probability of drawing a black ball from bag 1	P(A/E1) = \$\frac(6)(10)\$ = \$\frac(3)(5)\$
5	Step	probability of drawing a black ball from bag 2	P(A/E2) = \$\frac(3)(7)\$
6	Formula:	Bayes theorem \$(P(E_1/A) = P(E_1) * P(A/E_1)) / (P(E_1) * P(A/E_1) + P(E_2) * P(A/E_2))\$
7	Step	Simplification	\$\frac(1)(2) \times \frac(3)(5) / \frac(1)(2) \times \frac(3)(5) + \frac(1)(2)\times(3)/(7)\$
8	Step	After simplification we get	\$\frac(7)(12)\$
9		Answer	D

Step

Type

Explanation

Answer

Problem

A bag I contains 4 white and 6 black balls while another Bag II contains 4 white and 3 black balls. One ball is drawn at random from one of the bags, and it is found to be black. Find the probability that it was drawn from Bag I by using bayes theorem.

Step

E1 be the event of choosing bag I, E2 the event of choosing bag II, and A be the event of drawing a black ball.

Step

probability of two events are equal

P(E1) = P(E2) = \$\frac(1)(2)\$

Step

probability of drawing a black ball from bag 1

P(A/E1) = \$\frac(6)(10)\$ = \$\frac(3)(5)\$

Step

probability of drawing a black ball from bag 2

P(A/E2) = \$\frac(3)(7)\$

Formula:

Bayes theorem \$(P(E_1/A) = P(E_1) * P(A/E_1)) / (P(E_1) * P(A/E_1) + P(E_2) * P(A/E_2))\$

Step

Simplification

\$\frac(1)(2) \times \frac(3)(5) / \frac(1)(2) \times \frac(3)(5) + \frac(1)(2)\times(3)/(7)\$

Step

After simplification we get

\$\frac(7)(12)\$

Answer

Tutor: Questions

Seq	Type	Question
1	Problem	What did you learn from this problem?
2	Clue	What did you learn from the clues?
3	Hint	What did you learn from the Hints?
4	Step	What did you learn from the Steps?
5	Step	How can we improve the Steps?

Seq

Type

Question

Audio

Problem

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Clue

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Hint

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Step

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Step

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