Register

TIFR CSE 2021 | Part A | Question: 4

• retagged by
1,119 views
1 votes
1 votes

What is the probability that at least two out of four people have their birthdays in the same month, assuming their birthdays are uniformly distributed over the twelve months?

  1. $\frac{25}{48}$
  1. $\frac{5}{8}$
  1. $\frac{5}{12}$
  1. $\frac{41}{96}$
  1. $\frac{55}{96}$
• retagged by
User Avatar

1 Answer

1 votes
1 votes
Answer $(D)$

$P(\text{Atleast two have same birthday month}) = 1 – P(\text{No one have birthday in the same month})$
$= 1 – \frac{12}{12}.\frac{11}{12}.\frac{10}{12}.\frac{9}{12}$

$= \frac{41}{96}$
User Avatar
Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

599
views
1 answers
1 votes
soujanyareddy13 asked Mar 25, 2021
599 views
TIFR CSE 2021 | Part A | Question: 10
Lavanya and Ketak each flip a fair coin (i.e., both heads and tails have equal probability of appearing) $n$ times. What is the probability that Lavanya sees more heads than ketak?In ... \right )$\sum_{i=0}^{n}\frac{\binom{n}{i}}{2^{n}}$
User Avatar
1.4k
views
2 answers
2 votes
soujanyareddy13 asked Mar 25, 2021
1,429 views
TIFR CSE 2021 | Part B | Question: 11
Suppose we toss a fair coin (i.e., both beads and tails have equal probability of appearing) repeatedly until the first time by which at least $\textit{two}$ heads and at least ... of coin tosses that we would have to make?$8$4$5.5$7.5$4.5$
User Avatar
641
views
1 answers
1 votes
soujanyareddy13 asked Mar 25, 2021
641 views
TIFR CSE 2021 | Part A | Question: 5
Let $n, m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\left \{ 1, 2,\dots, n \right \}$ of size $k$. Consider sampling a ... 1-\frac{k!\binom{n}{k}}{n^{k}}$1-\frac{k!\binom{n}{k}}{m^{k}}$
User Avatar
847
views
1 answers
1 votes
soujanyareddy13 asked Mar 25, 2021
847 views
TIFR CSE 2021 | Part A | Question: 6
A matching in a graph is a set of edges such that no two edges in the set share a common vertex. Let $G$ be a graph on $n$ $\textit{vertices}$ in which there is a subset $M$ ... \right )^{m}$1-\left ( 1-p\left ( 1-p \right ) \right )^{m}$
User Avatar
Link Copied!