There are 52 cards in a deck. Each card contains a letter or a number. Theo selects a card at random, records the letter or number, and puts the card back in the deck. The results of his first six trials are: 5, Ace, 2, 8, Queen, and 9. Using Theo's results, how many number cards will he select in 24 trials?

Explanation:

A = ace

Q = queen

Theo's results are: 5, A, 2, 8, Q, 9

He got four numbers (5,2,8,9) out of 6 cards total. The empirical probability of getting a number is 4/6 = 2/3. Multiply this with the 24 trials to get (2/3)*24 = 48/3 = 16.

We expect Theo to get roughly 16 numbers if he conducted 24 trials. This is not guaranteed because of the nature of the random process. Though it should be fairly close to 16 assuming that we stick with that empirical probability (i.e. the amount of number cards is roughly 2/3 of the deck).

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.