###### Operating-Systems

October 11, 2023###### GATE 2021 CS-Set-1

October 11, 2023# GATE 2021 CS-Set-1

Question 8 |

The probability that at least two chocolates are identical is _____

0.81225 | |

0.4235 | |

0.6976 | |

0.3024 |

There are 5 bags having identical sets of 10 distinct chocolates. one chocolate is drawn from each bag, probability to find at least 2 chocolate is identical

The total number of such selections possible = 10*10*10*10*10 = 10^5.

We need to select such that at least two of them are identical.

We can count the number of ways with no chocolate being repeated and subtract it from total possible ways to get the required probability.

The number of ways to select all different/distinct = 10*9*8*7*6

Required number of selections= 10^5-10*9*8*7*6 = 69760

Required probability = 69760/10^5 = 0.69760

There are 5 bags having identical sets of 10 distinct chocolates. one chocolate is drawn from each bag, probability to find at least 2 chocolate is identical

The total number of such selections possible = 10*10*10*10*10 = 10^5.

We need to select such that at least two of them are identical.

We can count the number of ways with no chocolate being repeated and subtract it from total possible ways to get the required probability.

The number of ways to select all different/distinct = 10*9*8*7*6

Required number of selections= 10^5-10*9*8*7*6 = 69760

Required probability = 69760/10^5 = 0.69760