You have a standard deck of 52 playing cards. If you draw two cards at random from the deck. Required:
a. What is the probability that they are both hearts?
b. Your cat ate one of the playing cards! Assuming that the eaten card was a diamond, what is the probability that two cards drawn randomly from the deck are both hearts?
c. Are the events two cards drawn at random are both heartsl and the missing card is a diamond) independent? Fully justify your answer with math.

Explained below.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

(a)

Compute the probability that the two cards selected are both hearts as follows:

Thus, the probability that the two cards selected are both hearts is 0.0588.

(b)

It is provided that one of the card was eaten and it was a diamond.

So, now there are 51 cards in the deck.

And of these 51 cards two are selected.

Compute the probability that the two cards selected are both hearts as follows:

Thus, the probability that the two cards selected are both hearts is 0.0612.

(c)

No, the events two cards drawn at random are both hearts and the missing card is a diamond are not independent.

This is because the probability of selecting two hearts is dependent on the total number of cards available.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

i would say true? if the unit was informational and it "refreshed your understanding", then true.