# Probability of X in Binomial Distribution B(20, 1/52)

• Firepanda
In summary, the conversation discusses calculating the binomial distribution and range space for a variable X representing the number of times a spade is drawn from a standard deck of 52 cards with replacement. The probability function is also mentioned and it is clarified that the probability of drawing a spade on any one draw is not 1/52. The range space is described as a list of all possible numbers of spades that can be drawn, which includes 0 and 1. The correct probability is also mentioned.

#### Firepanda

http://img262.imageshack.us/img262/4669/rangevu0.jpg [Broken]

Ok so I think its asking for a binomial distribution of B(20, 1/52)

Would this be the probability function of X?

Also the range space of X is asked in a lot of these questions, but I've no idea on how to calculate it. I thought it was the codomain, so perhaps it's

20C0 * (1/52)^0 * (51/52)^20 = 0.678

20C20 * (1/52)^20 * (51/52)^0 = 4.79*10^-35

As the range. But it seems a little wrong :P

Any help is appreciated as my exam is tomorow!

Thx

Last edited by a moderator:
The variable X is "the number of times a spade is drawn when a card is chosen from a standard deck of 52 cards with replacement."

Yes, the probability function is the binomial distribution- but the probability of a spade on anyone draw is not "1/52"- that would be the probability of a specific card. How many spades are there in the deck?

And the range asked about is the range of X, not the range of the probability distribution. That is, you want to give a list of all the possible numbers of times you can draw a spade in this way. For example, it is quite possible that none of the draws will be a spade isn't it? So "0" is in the range space. It is quite possible that you get a single spade and the rest of the draws are not spades. So "1" is in the range space. Continue that reasoning.

HallsofIvy said:
The variable X is "the number of times a spade is drawn when a card is chosen from a standard deck of 52 cards with replacement."

Yes, the probability function is the binomial distribution- but the probability of a spade on anyone draw is not "1/52"- that would be the probability of a specific card. How many spades are there in the deck?

And the range asked about is the range of X, not the range of the probability distribution. That is, you want to give a list of all the possible numbers of times you can draw a spade in this way. For example, it is quite possible that none of the draws will be a spade isn't it? So "0" is in the range space. It is quite possible that you get a single spade and the rest of the draws are not spades. So "1" is in the range space. Continue that reasoning.

So the range space is just {0,1,2...,19,20}? :)

And yes sorry the probability isn't 51/52, I wasnt thinking properly :)