Question

Q.1a Suppose you go into an ice cream shop every day. Every day, you ask them for a uniformly random flavor of ice cream, independent of those chosen on previous days. Since you are such a regular customer, they are willing to abide your strange request. The ice cream parlor has 30 different flavors of ice cream, and each of the 30 flavors are offered every day. What is the probability that after 8 days, you have tried at least 7 unique flavors of ice cream?

It is fine to leave your answer in mathematical notation.

Q.A. B, C are playing a game. They each roll a 6-sided die. A player wins the game if the value of their die roll lies strictly in between the other two players. What is the probability that B wins the game?

Answer 1

Hello Sir/ Mam

We are most delighted to answer, but I would request you to please ask atmost 1 question or 4 subparts per post. Your cooperation will be highly appreciated. Thanks!

Q.1a

Required : P(at least 7 unique flavors of ice cream have tried)

For this, we have to calculate in how many ways we can select atleast 7 unique flavours in 8 days.

We will break it into 2 parts:

1. We select 7 unique flavours.

2. We select 8 unique flavours.

For 8 unique flavours, on the first day, we have 30 choices, on second day, we have 29, on third, we have 28, on 4th, 27 and so on....

Hence, total number of ways = 30*29*28*27*26*25*24*23

For 7 unique flavours, similarly we can choose 7 unique flavours on 7 days in 30*29*28*27*26*25*24 ways and we can repeat any one of these 7 on the 8th days.

Hence, total number of ways = 30*29*28*27*26*25*24*7

We can select 8 ice-creams from 30 in 30⁸ ways.

Hence, your required probability :

I hope this solves your doubt.

Do give a thumbs up if you find this helpful.