Question

You have also set up a card game in which a player picks a card from a standard deck of 52 cards. The player wins if these two events occur together: E1, in which the card drawn is a black card, and E2, in which the card drawn is a numbered card, 2 through 10.What is the probability of getting a black card and a numbered card? Calculate the probabilities P(E1) and P(E2) as fractions.

Answer 1

First, let's count:

there are 26 possible outcomes for E1 (black card)

there are 4x9 = 36 possible outcomes for E2, to pick a numbered card (any color)

there are 2x9 =18 possible outcomes for E1 (black) AND E2 (numbered, spade + clower)

the probability of E1 AND E2 is the ratio of the count of possible outcomes for E1 + E2 and the count of all possible outcomes (52 choices to pick a card from the deck):

P(E1 and E2) = 18/52 (34.6%)

And as asked:

P(E1) = 26/52 = 1/2 (50%)

P(E2) = 36/52 = 9/13 (69.2%)

Answer 2

`n (S) = 5\\ n (E_1) = 2 x 13 = 26\\P (E_1) (n (E_1))/(n (S)) = \frac {26}{52} = (1)/(2) \\\\ n (E_2) 4 x 9 = 36\\P (E_2)(n (E_2))/(n (S))=(36)/(52)= (9)/(13)`

EDMENTUM / PLATO ANSWER!!!!!!!!

CAN JUST WRITE:

`P (E_1) (n (E_1))/(n (S)) = \frac {26}{52} = (1)/(2)` = (50%)

`P (E_2)(n (E_2))/(n (S))=(36)/(52)= (9)/(13)` = (69.2%) :)))))