Question

A standard deck of 52 cards has four 13-card suits: diamonds, hearts, clubs, and spades. The diamonds and hearts are red, and the clubs and spades are black. Each 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king, and an ace. The jack, queen, and king are called face cards.

An experiment consists of randomly drawing a card from a standard deck. What is the probability that the card drawn is red and even? This is the last question in my homework due at 12:00 and if I get it wrong I have to start all ten over again PLEASE HELP

Answer 1

Hint: whether a given card is red and the number on the card is even are both independent events.
\[P(\text{red AND even})=P(\text{red})\times P(\text{even})\]

Answer 2

In that case it would be 26*18 right? since you exclude all of the face cards

Answer 3

wait that isnt right it would be 1/26 *1/18 lol but that still probably isnt right

Answer 4

\(\dfrac{26}{52}\) cards are red (13 hearts and 13 diamonds) and \(\dfrac{20}{52}\) are even (the 2,4,6,8,10 of each suit).

Answer 5

ok so you would multiply the two together to get 10...?

Answer 6

Probabilities can only be numbers between 0 and 10. You have to divide by 52 twice.
\[\frac{26}{52}\times\frac{20}{52}=\frac{20\times26}{52^2}\]

Answer 7

oooooooh sweet so simplified it would be 5/26

Answer 8

Hey thanks a ton I understand it a lot better now

Answer 9

Yes, you're welcome