Probability · Mathematics · IAT (IISER)
MCQ (Single Correct Answer)
1
Five fair coins are tossed independently. What is the probability that at least two heads appear?
IAT (IISER) 2025
2
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?
IAT (IISER) 2024
3
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?
IAT (IISER) 2023
4
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?
IAT (IISER) 2022
5
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 :
IAT (IISER) 2020