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Q1
There are two stores, A and B, which sell t-shirts on the market. Store A has stock of red and black t-shirts, and store B has stock of red and black t-shirts. One of the stores is selected at random and two t-shirts are purchased without replacement from that store. Given that both the t-shirts purchased are red, the probability that they were purchased from store A is . Find the value of .
Integer answer
Q2
Three independent draws are made from a standard deck of playing cards, with replacement and reshuffling between each draw. Which of the following statements is/are correct?
Multiple correct
Q3
A bakery sells bread, cake, and pastry each day. Of the total items sold, are bread, are cake, and are pastry. Each individual item has a probability of being defective, either stale or burnt, independent of its type. One item is selected at random from the total items sold that day. Define the events : the selected item is stale or burnt, and : the selected item is cake. Which of the following options is/are correct?
Multiple correct
Q4
Find the probability that the committee contains exactly one girl, given that it contains at least one boy.
Comprehension
Q5
Find the value of . Enter the answer correct to two decimal places.
Comprehension
Q6
If , and , what is the value of ?
Single correct
Q7
A box contains white balls and black balls, while box contains white balls and black balls. One ball is randomly selected from box and transferred to box . After the transfer, one ball is drawn at random from box . What is the probability that the ball drawn from box is black? Enter the answer correct to three decimal places.
Integer answer
Q8
Given that the first draw results in gold coins and silver coin, what is the probability that the second draw results in exactly silver coins and at least gold coin?
Comprehension
Q9
Which of the following option(s) is/are correct?
Comprehension
Q10
Consider an experiment of rolling a fair four-sided die twice where all possible outcomes are equally likely. Define the events : first roll results in , : sum of the two rolls is , and : second roll results in . Which among the following statements are true?
Multiple correct
Q11
A card is randomly drawn from a standard deck of playing cards. If the chosen card is known to be a face card (King, Queen, or Jack), what is the probability that it is also an Ace?
Integer answer
Q12
What is the probability that a randomly selected student passes the test? Enter the answer correct to two decimal places.
Comprehension
Q13
If a randomly selected student is known to have passed the test, what is the probability that this student is a member of the Science Club? Enter the answer correct to two decimal places.
Comprehension
Q14
An urn contains white and black chips and another urn contains white and black chips. One urn is selected at random and a chip is drawn from it. If the chip drawn is found black, find the probability that the urn chosen was . Enter the answer correct up to decimal places.
Integer answer
Q15
In a school with students, students are enrolled in Math, students are enrolled in Science, and students are enrolled in both Math and Science. If a student is randomly selected, what is the probability that he/she is enrolled in Science given that he/she is enrolled in Math?
Single correct
Q16
Which of the following options is/are correct?
Multiple correct
Q17
Which of the following option(s) is/are true?
Multiple correct
Q18
Find the probability that a randomly chosen passenger gets a taxi with engine issues. Enter the answer correct to three decimal places.
Comprehension
Q19
Given that a passenger gets a taxi with engine issues, find the probability that the passenger took a ride with the Green taxi company. Enter the answer correct to two decimal places.
Comprehension
Q20
Are the events and independent?
Comprehension
Q21
Which of the following option(s) is/are correct?
Multiple correct
Q22
What is the probability that both are boys given that at least one is a boy? Enter the answer correct to two decimal places.
Comprehension
Q23
What is the probability that co-education will be introduced in the college?
Comprehension
Q24
If co-education has been introduced in the college, then what is the probability that is principal? Enter the answer correct to two decimal places.
Comprehension
Q25
A fair die is rolled twice and a fair coin is tossed twice. Define events and as follows: : a three appears on the die twice. : a head appears on the coin twice. Find the value of .
Single correct
Q26
What is the probability that Suman will win the colour TV?
Comprehension
Q27
If she wins a colour TV, then what is the probability that candy was from bag ? Enter the answer correct to two decimal places.
Comprehension
Q28
Consider an experiment of rolling a fair four-sided die twice where all the possible outcomes are equally likely. Define the events: first roll results in a , sum of the two rolls is , and second roll results in a . Which among the following statements are true?
Multiple correct
Q29
A person is randomly picked from this group. What is the probability that the person is a female, given that the person's reaction is favourable to the new gadget? Enter the answer correct to two decimal places.
Comprehension
Q30
Ajay speaks truth in cases, while Vijay speaks truth in cases. What is the probability that Ajay and Vijay will contradict in stating the same fact?
Integer answer
Q31
A blood test indicates the presence of Amyotrophic lateral sclerosis (ALS) of the time when ALS is actually present. The same test indicates the presence of ALS of the time when ALS is not actually present. One percent of the population actually has ALS. Calculate the probability that a person actually has ALS given that the test indicates the presence of ALS. Enter your answer correct to two decimal places.
Integer answer
Q32
Parcels from sender to receiver pass sequentially through two post offices. The first post office has probability of losing an incoming parcel, and the second post office has probability of losing an incoming parcel, independently of all other parcels. Given that the parcel is lost, find the probability that it was lost by the second post office. Enter the answer correct to 2 decimal accuracy.
Integer answer
Q33
An urn contains cards numbered to . One card is drawn at random. Define events: : the number on the card is greater than but less than or equal to ; : the number is greater than or equal to but less than ; : the number is greater than but less than or equal to . Which statement(s) is/are true?
Multiple correct
Q34
A box contains numbered balls such that red coloured balls are numbered to and black coloured balls are numbered to . If a randomly chosen ball is even numbered, then what is the probability that the selected ball is of red colour? Enter the answer correct to two decimal accuracy.
Integer answer
Q35
What is the probability that an email is detected as spam? Enter the answer correct to two decimal accuracy.
Comprehension
Q36
If the email is detected as spam, then what is the probability that it is in fact a non-spam email? Enter the answer correct to two decimal accuracy.
Comprehension
Showing 36 questions.