Question

You select a card at random. Without replacing the card, you select a second card. Find the probability.

M A T H E M A T I C S

P(M, then H)
A. 3 /11
B. 2/21
C. 1/55
D. 2/121

Answer 1

is there more information to this problem?
for example what kind of cards are being selected?

Answer 2

what is on the cards

Answer 3

M A T H E M A T I C S

Answer 4

ok so there are a total of 11 cards?
each one has a letter that makes up the word MATHEMATICS?

Answer 5

Yes

Answer 6

ok so we need to find the probability of selecting an M and then an H

Answer 7

ok so what is the probability of selecting an M on the first draw?

Answer 8

I think that the question. I can't pin point it

Answer 9

it will be equal to the number of cards with an M divided by the total number of cards

Answer 10

ok so how many cards have an M?
M A T H E M A T I C S
there is one card for each letter

Answer 11

2

Answer 12

P(draw an M) = (number favorable to drawing an M) / (number of cards total), to re-phrrase Miracrown = \frac{2}{11}

Answer 13

\[\frac{2}{11}\]

Answer 14

yyes
and there are a total of 11 cards
so the probability of choosing an M as the first card is 2/11
now we need to find the probability of choosing an H when we choose a second card

Answer 15

How many H cards are there? 1 right?
right now remember we don't replace the cards once we have chosen them, so there are 10 cards left since we chose one already for the first draw
so the probability of choosing an H on the second draw is 1/10
since there are 10 cards left, only 1 is an H
so the probability of selecting an M as the first card and an H as the second is 2/11 times 1/10

Answer 16

so the probability of selecting an M as the first card and an H as the second is 2/11 times 1/10
remember P(A and B) = P(A) times P(B) when the events A and B are independent as they are here
here A = choosing an M as the first card
B = choosing H as the second given we chose an M as the first

Answer 17

actually they arent really independent, but we can still use that formula

Answer 18

2/11 times 1/10 = 11/55
1/55

Answer 19

Alright! Thank you >_<

Answer 20

so the answer is C

Answer 21

yw :]

Answer 22

\[P(AB) = P(B)P(B|A)\] works for independent and dependent (if independent P(B given A) = P(B)

Answer 23

^^ only formula to memorize cuz it applies to both

Answer 24

sorry that should be \[P(A)P(B|A)\]