Question

simon rolls a number cube and picks a card from a standard deck. let event e be rolling an even number and event k be picking a king from the deck. match each notation to its meaning.

• \\(p(k \cup e)\\)
• \\(p(k)\\)
• \\(p(e)\\)
• \\(p(e \cap k)\\)

meanings:

• the probability of rolling an even number
• the probability of picking a king or rolling an even number
• the probability of picking a king
• the probability of rolling an even number and picking a king

Explanation:

Define the events and notation

Using the Theoretical Probability knowledge point

• Let \(E\) represent the event of rolling an even number.
• Let \(K\) represent the event of picking a king.
• The notation \(P(A)\) represents the probability of event \(A\) occurring.

Match single event probabilities

Using the Theoretical Probability knowledge point

• \(P(K)\) represents the probability of event \(K\) occurring, which is:

"the probability of picking a king"

• \(P(E)\) represents the probability of event \(E\) occurring, which is:

"the probability of rolling an even number"

Match compound event union

Using the Probability Addition Rule knowledge point

• The symbol \(\cup\) represents the union of two sets or events (logical "OR").
• Therefore, \(P(K \cup E)\) represents:

"the probability of picking a king or rolling an even number"

Match compound event intersection

Using the Probability Multiplication Rule knowledge point

• The symbol \(\cap\) represents the intersection of two sets or events (logical "AND").
• Therefore, \(P(E \cap K)\) represents:

"the probability of rolling an even number and picking a king"

Answer:

Notation	Meaning
\(P(K)\)	the probability of picking a king
\(P(E)\)	the probability of rolling an even number
\(P(E \cap K)\)	the probability of rolling an even number and picking a king