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Ques 11 GATE 2021
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.
The probability that at least two chocolates are identical is
(c) is the correct answer.
Ques 12 Gate 2018
A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?
(Probability) is the correct answer.
Ques 13 GATE 2018
A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident.
(i) 85% of cabs in the city are green and the remaining cabs are blue.
(ii) A witness identified the cab involved in the accident as blue.
(iii) It is known that a witness can correctly identify the cab colour only 80% of the time.
Which of the following options is closest to the probability that the accident was caused by a blue cab?
(c) is the correct answer.
Ques 14 GATE 2017 SET-2
An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is
(a) is the correct answer.
Ques 15 Gate 2017 Set-1
The probability that a k-digit number does NOT contain the digits 0, 5 or 9 is__
(c) is the correct answer.
Ques 16 GATE 2017 SET-1
Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place)
(0.0277) is the correct answer.
When three fair dice are thrown simultaneously, we need to find the probability that all three show the same number.
A fair die has 6 possible outcomes (1, 2, 3, 4, 5, 6).
When three dice are thrown together, the total number of possible outcomes is:
6 × 6 × 6 = 216
Now let me count the favorable outcomes where all three dice show the same number:
(1, 1, 1) - all three show 1
(2, 2, 2) - all three show 2
(3, 3, 3) - all three show 3
(4, 4, 4) - all three show 4
(5, 5, 5) - all three show 5
(6, 6, 6) - all three show 6
So there are 6 favorable outcomes.
The probability is calculated as:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 6/216
Probability = 1/36
Probability = 0.027777...
Rounding to three decimal places:
Answer: 0.028 (or 0.027)
Ques 17 GATE 2016 SET-1
A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?
(c) is the correct answer.
Ques 18 GATE 2016
Shaquille O' Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts?
(a) is the correct answer.
Ques 19 GATE 2014 SET-3
A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is
(0.81) is the correct answer.
Ques 20 GATE 2014 SET-3
A group consists of equal number of men and women. Of this group, 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______
(0.65) is the correct answer.
Ques 21 GATE 2014 SET-2
A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1 → 0.167; 2 → 0.167; 3 → 0.152; 4 → 0.166; 5 → 0.168; 6 → 0.180. We call this die
(b) is the correct answer.
Ques 22 GATE 2014 SET-2
A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence:
1 → 0.167; 2 → 0.167; 3 → 0.152; 4 → 0.166; 5 → 0.168; 6 → 0.180. We call this die
(b) is the correct answer.
Ques 23 GATE 2014 SET-1
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is
(b) is the correct answer.