Exams › JEE Main › Physics
A ship has three independent engines E1, E2, and E3 that operate with probabilities 1/2, 1/4, and 1/4 respectively. The ship is operational if at least two engines function. Let X be the event that the ship is operational. Which of the following are true?
- P(E1 does not function | ship is operational) = 3/16
- P(exactly two engines are functioning) = 7/8
- P(ship is operational | E2 is functioning) = 5/16
- P(ship is operational | E1 is functioning) = 7/16
Correct answer: P(ship is operational | E1 is functioning) = 7/16
Solution
P(X) = (1/2)(1/4)(1/4) + (1/2)(1/4)(3/4) + (1/2)(3/4)(1/4) + (1/2)(1/4)(1/4) = 1/32 + 3/32 + 3/32 + 1/32 = 8/32 = 1/4. Then evaluate each option using conditional probability.
Related JEE Main Physics questions
- Two urns contain coloured balls: Urn-I has 4 red and 2 white balls; Urn-II has 2 red and 4 white balls. One ball is drawn at random from Urn-I. If it is red, it is placed in Urn-II; if it is white, it is returned to Urn-I along with one extra white ball taken from Urn-II. Next, one ball is drawn at random from Urn-II. If it is red, it is returned to Urn-II along with one extra red ball taken from Urn-I; if it is white, it is placed in Urn-I. After this pair of operations, it is observed that either the number of white balls in Urn-I is the same as initially, OR the number of red balls in Urn-I is the same as initially. Let p be the probability that the number of red balls in Urn-I remained the same as initially. Find the value of 17p.
- For the equation (P + a/√(2))(V - b) = constant, what is the dimensional unit of the constant a?
- A body has a measured mass of 5.00 ± 0.05 kg and a measured volume of 1.00 ± 0.05 m³. What is the maximum possible percentage error in its density?
- A substance has a density of 4 g/cm³ in the CGS system. If a new unit system is used where the unit of length is 10 cm and the unit of mass is 100 g, what is the numerical value of the density in that system?
- Which of the following physical quantities has dimensions that do not match the other three?
- If the percentage uncertainties in measuring mass M, length L, and time T are 1%, 1.5%, and 3% respectively, what is the percentage error in a quantity having dimensions M L⁻¹ T⁻¹?
⚔️ Practice JEE Main Physics free + battle 1v1 →