Question

cards example
multiple choice 1 point
you draw a random card from the above deck of cards and notice only that it is white. which of the following represents the probability that the card has suit y?
p(suit y and white)
p(suit y | white)
p(white | suit y)
p(suit y)
numeric 1 point
you draw a random card from the above deck of cards and notice only that it is white. what is the probability that the card has suit y?
answer
enter your answer as a decimal.

Explanation:

Step1: Count total white - cards

There are 10 white - cards (5 in suit Y and 5 in suit X).

Step2: Count white - cards in suit Y

There are 5 white - cards in suit Y.

Step3: Calculate the conditional probability

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of "probability that the card has suit Y given that it is white", let $A$ be the event of having suit Y and $B$ be the event of being white. The number of elements in $A\cap B$ (white cards in suit Y) is 5, and the number of elements in $B$ (white cards) is 10. So $P(\text{suit Y}|\text{white})=\frac{5}{10}=0.5$.

Answer:

0.5