Question

question 3 1 pts if we draw a card from a standard deck, how to calculate this probability: p(drawing any king | the draw is a spade)? 1/52 4/52 4/13 1/13

Explanation:

Step1: Identify relevant card - counts

A standard deck has 52 cards. There are 13 spades in a deck and 1 king of spades. The conditional - probability formula is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of counting problems, $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of events $A$ and $B$, and $n(B)$ is the number of elements in event $B$. Here, event $A$ is drawing a king and event $B$ is drawing a spade. The number of cards that are both a king and a spade ($n(A\cap B)$) is 1, and the number of spades ($n(B)$) is 13.

Step2: Calculate the probability

Using the formula $P(A|B)=\frac{n(A\cap B)}{n(B)}$, we substitute $n(A\cap B) = 1$ and $n(B)=13$. So $P(\text{drawing any king}|\text{the draw is a spade})=\frac{1}{13}$.

Answer:

D. 1/13