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IITM BS Week 8 Statistics 1 Questions | Prasnya

Statistics 1 > Week 8

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13Q

There are two bags, Bag A and Bag B. Bag A contains 2 red balls and 1 blue ball, while Bag B contains 1 red ball and 2 blue balls. The probability of choosing Bag A is

\frac{1}{3}

, and the probability of choosing Bag B is

\frac{2}{3}

. After selecting a bag, one ball is drawn from it. What is the probability that the ball drawn is red?

21 December 2025

In a class, a teacher assigns a query to three students. Each student attempts to solve the query independently. The probabilities that they are able to solve it correctly are

\frac{1}{4}

\frac{1}{5}

\frac{1}{2}

respectively. Find the probability that the query gets solved by at least one student. Enter the answer correct to one decimal place.

At a university, 60% of the students are enrolled in science programs, while 40% are enrolled in arts programs. Among science students, 25% participate in research projects, whereas 15% of arts students participate in research project. If a student is chosen at random, what is the probability that he/she participates in a research project? Enter the answer correct to two decimal places.

A jar contains 5 red balls and 7 blue balls. Two balls are drawn without replacement. Let event A be the event that the first ball drawn is red, and event B be the event that the second ball drawn is blue. Which of the following statement(s) is(are) true?

Multiple correct

22 December 2024

Suppose person A makes accurate predictions about the weather with a probability of

\frac{4}{7}

and person B makes accurate predictions about tomorrow's weather with a probability of

\frac{2}{3}

. If you ask both of them their predictions about tomorrow's weather, what is the probability that their predictions will be contradictory? Enter the answer correct to two decimal places.

01 September 2024

Find the probability that a patient has the disease given that the test is positive. Enter the answer correct to two decimal places.

A fair coin is repeatedly tossed until two consecutive tosses result in the same outcome. What is the probability that the experiment ends in three tosses? Enter the answer correct to two decimal places.

24 December 2023

What is the probability that the selected coin lands on head? Enter the answer correct to three decimal places.

24 December 2023

If the selected coin lands on head, what is the probability that the coin is fair? Enter the answer correct to one decimal place.

24 December 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)

\frac{17}{36}

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

03 September 2023

Samsung mobile company launched two new phones, Galaxy A03 and Galaxy S22. The probability that Galaxy A03 has good battery life is 70% and the probability that Galaxy S22 has good battery life is 80%. If a phone is selected randomly, then what is the probability that it has a good battery life? (Enter the answer correct to 2 decimal accuracy).

11 December 2022

An analyst did a survey to know about annual incomes of recent graduates of two different universities and the results are given in Table Q.1. If a randomly selected graduate earns more than $40,000, then what is the probability that he/she is from University B?

What is the value of

P(X \le 3 \mid X > 3)

Showing 13 questions.

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