Question

Laura has decided to offer a meeting at her house as her birthday. For this, it has prepared several quantities of 3 types of cocktails: tom collins, cubalibre, mojito
The dynamics that Laura uses for her guests to choose the drinks is to pack the cocktails in dark glasses so that their selection is completely random. Furthermore, it has been established that the selection must be independent of the previous one.
The probability of choosing each of the cocktails is given by a survey that Laura made to 30 of her friends, the answers to which are presented below:
1. 4 people showed liking for the 3 types
2. 8 people like both tom collins and cubalibre
3. 11 like both tom collins and mojito
4. 2 people like only the mojito
5. 4 people like only the tom collins
6. 3 people like only the cubalibre

Assume that each of the surveyed friends showed a taste for one or more cocktails.

If the first 3 cocktails were selected there was one of the tom collins, find the probability that the eighth cocktail selected is the fourth of the cocktail tom collins?

Answer 1

Given that out of the first three cocktails that were selected one of the cocktail was tom collins,we need to find the probability that the eighth cocktail selected is the fourth of the cocktail tom collins.

Which means that out of 8 cocktails tom collins should occur four times and the eighth cocktail should be tom collins

So,

By using combination formula that is =   

P(eighth cocktail selected being the fourth tom collins) =

=

=

= =

=   

=

=

=   

=   

0.17

Hence the probability that the eighth cocktail selected is the fourth of the cocktail tom collins is 0.17