a box contains 100 cards, of which 25 are numbered 1, 35 are numbered 2, 30 are numbered 3, 10 are numbered 4. One card will be drawn from the box and its number X observed. Give the probability distribution of X
How in the world do I do this?
do I have to manually get the probabilites or is there a forumla I can use?
nevermind I don't need help.
First make a table of probabilties.
P(x=1) = 0.2
P(x=2) = 0.35
P(x=3) = 0.30
P(x=4) = 0.15
Now do a distribution plot, which is the likelihood of one of the four card types being drawn. P on y, x on x-axis etc.
34
It seems like you have already figured out how to solve the problem on your own. However, I can still explain the process for finding the probability distribution of X, in case you're interested.
To find the probability distribution of X, you need to calculate the probability of drawing each possible number from the box. The formula you can use is:
P(X = x) = Number of cards numbered x / Total number of cards in the box
In this case, we have the following numbers of cards:
- 25 cards numbered 1
- 35 cards numbered 2
- 30 cards numbered 3
- 10 cards numbered 4
The total number of cards in the box is 100. Using the formula, we can calculate the probabilities:
P(X = 1) = 25/100 = 0.25
P(X = 2) = 35/100 = 0.35
P(X = 3) = 30/100 = 0.3
P(X = 4) = 10/100 = 0.1
So, the probability distribution of X is:
P(X = 1) = 0.25
P(X = 2) = 0.35
P(X = 3) = 0.3
P(X = 4) = 0.1
This means that there is a 25% chance of drawing a card numbered 1, a 35% chance of drawing a card numbered 2, a 30% chance of drawing a card numbered 3, and a 10% chance of drawing a card numbered 4.
If you have any further questions, feel free to ask!