IAT (IISER) 2024 | Probability Question 2 | Mathematics

A ship sets off on a voyage with three engines, labelled $A, B$, and $C$, which work independently. The ship can complete the voyage only if at least two of these engines keep working. The probability that engine $A$ breaks down is $1 / 4$, that engine $B$ breaks down is $1 / 4$, and that engine $C$ breaks down is $1 / 2$. What is the probability that the ship can complete the voyage?

3/4

$1 / 2$

$1 / 32$

$1 / 4$

IAT (IISER) 2023

MCQ (Single Correct Answer)

-1

Consider three biased coins. Let the probability of getting head be $\frac{1}{3}$ and the probability of getting tail be $\frac{2}{3}$ in each of the coins. Consider the experiment of tossing the threee coins one by one, and the following events: $E$ :"At least two heads show up" F:"First coin shows tail". What is the conditional probability of $E$ given that $F$ has already occurred?

$1 / 9$

$2 / 9$

$1 / 4$

$4 / 9$

IAT (IISER) 2022

MCQ (Single Correct Answer)

-1

A randomly chosen card from a deck of 52 cards is given to be a black card (Spade or Club). What is the probability that it is either a face card (King, Queen or Jack) or a Spade?

$7 / 13$

$8 / 13$

9/13

$19 / 26$

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

A bag contains 8 balls, of which 5 are green and 3 are red. The probability that two balls chosen at random are of the same colour is :

$12 / 28$

$14 / 28$

$15 / 28$

$13 / 28$

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