Question

A radio station has 10 free tickets to a concert to give away. Each listener may send in one email requesting a ticket. Emails are received from 1300 listeners. Emails are then selected at random one at a time until all tickets are given away. The first 9 tickets have been given away. Joseph’s email has not been selected. What is Joseph’s probability of winning the last ticket?

Answer 1

ǫᴜᴇsᴛɪᴏɴ →

A radio station has 10 free tickets to a concert to give away. Each listener may send in one email requesting a ticket. Emails are received from 1300 listeners. Emails are then selected at random one at a time until all tickets are given away. The first 9 tickets have been given away. Joseph’s email has not been selected. What is Joseph’s probability of winning the last ticket?

ᴀɴsᴡᴇʀ →

Given : A radio station has 10 free tickets to a concert to give away.

Each listener may send in one email requesting a ticket.

Emails are received from 1200 listeners.

Emails are then selected at random one at a time until all tickets are given away.

first 9 tickets have been given away.

John’s email has not been selected.

To Find : John’s chance of winning the last ticket

Solution:

Total Emails = 1200

Already selected = 9

Remaining Emails = 1200 - 9 = 1191

John’s chance of winning the last ticket is 1 in 1191

Probability of John’s winning the last ticket

$\longmapsto\tt{\dfrac{1}{1191}}$