# [ASK] Probability of Getting the Main Doorprize

#### Monoxdifly

##### Well-known member
There's an event which is joined by 240 members. The Event Organizer prepares 30 doorprize with one of them being the main ones. If Mr. Aziz's family has 15 tickets, the probability that Mr. Aziz gets the main doorprize is ....
A. 1/16
B. 1/8
C. 1/4
D. 1/2

I thought the answer was 15/240 (the probability of Mr. Aziz's family getting the doorprize) times 1/30 (the main one among the doorprize) and it results in 1/480, but it's not in the options. Is the book wrong or am I the one who miscalculated?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Hi Mr. Fly!

I'm assuming those 30 doorprizes are divided randomly among the 240 members.
And that the 15 tickets in Mr. Aziz's family correspond to 15 members.
And that there is only 1 main doorprize.
Just checking, is it a typo that you write 'the main ones' as plural?
Otherwise it suggests that there is more than 1 main doorprize.

If there is only 1 main prize, and Mr. Aziz has 15 chances out of 240 on it, then the probability that Mr. Aziz gets the main doorprize is 15/240 = 1/16.

Note that if my interpretation is correct, we can expect that Mr. Aziz's family collects $\frac{15}{240 }\cdot 30$ door prizes as opposed to the 15/240 that you suggested.
Since only 1 of them is the main prize, we multiply indeed by 1/30, resulting in the $\frac{15}{240}\cdot 30\cdot \frac{1}{30}=\frac{15}{240}=\frac{1}{16}$ that I already mentioned.

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#### HallsofIvy

##### Well-known member
MHB Math Helper
I see no reason to even consider the "30 door prizes". The question is only about the one main prize. There are 240 people and 15 of them are in this family. The probability of someone in this family winning the one main prize is $$\frac{15}{240}= \frac{1}{16}$$.

#### Monoxdifly

##### Well-known member
Thank you, both of you. And yes, Klaas, that was a typo.
It has been quite a long time since someone calls me Mr. Fly...