IITM BS Question 10 - Week 8 Practice

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IITM BS Question 10 - Week 8 Practice | Prasnya

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Q10Numerical4 Marks3 Sep 2023

A shopkeeper has two boxes of chocolates. Box-1 contains 5 dark chocolates and 4 white chocolates, while box-2 contains 3 dark chocolates and 3 white chocolates. A customer visits the shop to purchase a chocolate. If the shopkeeper randomly chooses a box and gives a chocolate from that chosen box, then what is the probability of the selected chocolate being white? (Enter the answer correct to two decimal places.) Let W be the event of selecting a white chocolate. -

P(W\mid B1) = 4 / (5+4) = 4/9 - P(W\mid B2) = 3 / (3+3) = \frac{3}{6} = \frac{1}{2}

By the Law of Total Probability:

P(W) = P(W\mid B1)P(B1) + P(W\mid B2)P(B2) P(W) = (4/9) \cdot (1/2) + (1/2) \cdot (1/2) = 2/9 + 1/4 = (8 + 9)

/36 =

\frac{17}{36}

≈ 0.4722. Rounding to 2 decimal places, we get 0.47 (accepted range: 0.43 to 0.51).

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Q10

00:00

3 Sep 2023

Statistics 1 · Week 8

Q10.A shopkeeper has two boxes of chocolates. Box-1 contains 5 dark chocolates and 4 white chocolates, while box-2 contains 3 dark chocolates and 3 white chocolates. A customer visits the shop to purchase a chocolate. If the shopkeeper randomly chooses a box and gives a chocolate from that chosen box, then what is the probability of the selected chocolate being white? (Enter the answer correct to two decimal places.) Let W be the event of selecting a white chocolate. -

P(W\mid B1) = 4 / (5+4) = 4/9 - P(W\mid B2) = 3 / (3+3) = \frac{3}{6} = \frac{1}{2}

By the Law of Total Probability:

P(W) = P(W\mid B1)P(B1) + P(W\mid B2)P(B2) P(W) = (4/9) \cdot (1/2) + (1/2) \cdot (1/2) = 2/9 + 1/4 = (8 + 9)

/36 =

\frac{17}{36}

≈ 0.4722. Rounding to 2 decimal places, we get 0.47 (accepted range: 0.43 to 0.51).

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Q10Numerical4 Marks3 Sep 2023

P(W\mid B1) = 4 / (5+4) = 4/9 - P(W\mid B2) = 3 / (3+3) = \frac{3}{6} = \frac{1}{2}

By the Law of Total Probability:

P(W) = P(W\mid B1)P(B1) + P(W\mid B2)P(B2) P(W) = (4/9) \cdot (1/2) + (1/2) \cdot (1/2) = 2/9 + 1/4 = (8 + 9)

/36 =

\frac{17}{36}

≈ 0.4722. Rounding to 2 decimal places, we get 0.47 (accepted range: 0.43 to 0.51).

Your answer

Press Enter to check.

Q10

00:00

3 Sep 2023

Statistics 1 · Week 8

P(W\mid B1) = 4 / (5+4) = 4/9 - P(W\mid B2) = 3 / (3+3) = \frac{3}{6} = \frac{1}{2}

By the Law of Total Probability:

P(W) = P(W\mid B1)P(B1) + P(W\mid B2)P(B2) P(W) = (4/9) \cdot (1/2) + (1/2) \cdot (1/2) = 2/9 + 1/4 = (8 + 9)

/36 =

\frac{17}{36}

≈ 0.4722. Rounding to 2 decimal places, we get 0.47 (accepted range: 0.43 to 0.51).

Your Answer

Save

Check

Details