Question

homework 5 - conditional probability: problem 8 (1 point) you must type your answer as fractions like 2/3 (you do not need to reduce or simplify). help (fractions) a standard deck of cards has 52 cards. each card has a suit (hearts, diamonds, clubs, or spades) and a rank (2 - 10, jack, queen, king, or ace). hearts and diamonds are red; clubs and spades are black. there is exactly one card with each suit - rank combination. if you draw a card from a shuffled deck, whats the probability of drawing a diamond? if you return the first card you drew, shuffle again, then draw a second card, whats the probability of drawing a black card? whats the probability that your first card is a diamond and your second card is black? note: you can earn partial credit on this problem. preview my answers submit answers

Explanation:

Step1: Calculate probability of drawing a Diamond

There are 13 diamonds in a 52 - card deck. Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So the probability of drawing a diamond is $\frac{13}{52}$.

Step2: Calculate probability of drawing a black card

There are 26 black cards in a 52 - card deck. So the probability of drawing a black card is $\frac{26}{52}$.

Step3: Calculate probability of first - diamond and second - black

Since the draws are independent events, the probability of two independent events $A$ and $B$ occurring is $P(A)\times P(B)$. The probability of drawing a diamond first is $\frac{13}{52}$ and the probability of drawing a black card second is $\frac{26}{52}$. So the probability of first - diamond and second - black is $\frac{13}{52}\times\frac{26}{52}$.

Answer:

$\frac{13}{52}$
$\frac{26}{52}$
$\frac{13\times26}{52\times52}$