Statistics for Data Science I Quiz 2: 4 August 2024 (May 2024 term)

Which of the following option(s) is(are) true?

A city has three main taxi companies: Red Taxi, Blue Taxi, and Green Taxi. Historical data shows that 20% of the passengers use Red Taxi, 50% use Blue Taxi, and 30% use Green Taxi. If 5% of the cars from Red Taxi, 4% from Blue Taxi, and 8% from Green Taxi have engine issues.
Based on the given information, answer the given subquestions.

Find the probability that a randomly chosen passenger gets a taxi with engine issues? Enter the answer correct to three decimal places.

A city has three main taxi companies: Red Taxi, Blue Taxi, and Green Taxi. Historical data shows that 20% of the passengers use Red Taxi, 50% use Blue Taxi, and 30% use Green Taxi. If 5% of the cars from Red Taxi, 4% from Blue Taxi, and 8% from Green Taxi have engine issues.
Based on the given information, answer the given subquestions.

Given that a passenger gets a taxi with engine issues, then find the probability that the passenger took a ride with the Green taxi company? Enter the answer correct to two decimal places.

There are 200 employees in a company. There are 40 employees who know Python language and 50 employees who know SQL. Out of these, there are 10 who know both Python and SQL. Let E1 be the event that a randomly selected employee knows Python and E2 be the event that a selected employee knows SQL.
Based on the given information, answer the given subquestions.

Are the events E1 and E2 independent?

There are 200 employees in a company. There are 40 employees who know Python language and 50 employees who know SQL. Out of these, there are 10 who know both Python and SQL. Let E1 be the event that a randomly selected employee knows Python and E2 be the event that a selected employee knows SQL.
Based on the given information, answer the given subquestions.

A committee of 7 members has to be formed from 9 Men and 4 Women.
Based on the given information, answer the given subquestions.

In how many ways can this be done when the committee consists of exactly 3 Women?

A committee of 7 members has to be formed from 9 Men and 4 Women.
Based on the given information, answer the given subquestions.

In how many ways can this be done when the committee consists of at least 3 Women?

In a hockey team consisting of 11 players, each player shakes hands with every other player exactly once before the match begins. How many handshakes occur among the teammates?

A box contains 3 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one red ball is to be included in the draw?

Praveen attempts a question paper of 12 questions. Each question has 4 choices. If he answers the questions randomly, then find the number of ways in which he can attempt the entire paper.

In a dinner party, there are 2 males and 5 females who need to be seated around a round table. In how many ways can they be seated so that no two males are seated next to each other?

Pramod goes to a shop to buy some clothes. Shopkeeper shows him 7 shirts, 4 pants and 12 t- shirts. If he selects three clothes at random, then find the probability that the randomly chosen clothes are of different type. (Enter the answer correct to two decimal places)