Question

If Event A is "the card is black" and Event B is "the card is a king," demonstrate the equation holds true.

Answer 1

`(1)/(52)=(1)/(4)*(4)/(52)`Step-by-step explanation:

Event A = the card is black

Event B = the card is a king

For the equation to hold true:

`\begin{gathered} P(A\text{ and B) = }P(A|B)* P(B) \\ P(\text{card is black and a king) = P(}card\textcard is king)*\text{ P(card is king)} \end{gathered}`
`\begin{gathered} \text{There are 4 kings in a deck} \\ P(A|B)\text{ = }(1)/(4) \\ P(B)=\text{ }(4)/(52) \\ P(A\text{ and B) = }(1)/(4)*(4)/(52)\text{ = }(1)/(52) \end{gathered}`
`\begin{gathered} \text{There are 26 blacks in a deck} \\ P(B|A)\text{ = }(1)/(26) \\ P(A)=\text{ }(26)/(52) \\ P(A\text{ and B) = }(1)/(26)*(26)/(52)\text{ = }(1)/(52) \end{gathered}`
`\begin{gathered} \text{Hence, the equation holds true:} \\ \text{for }P(A\text{ and B) = }P(A|B)* P(B) \\ (1)/(52)=(1)/(4)*(4)/(52) \\ \end{gathered}`