Two cards will be dealt off the top of a well-shuffled deck....

Two cards will be dealt off the top of a well-shuffled deck. You have a choice:
(i) To win $\$ 1$ if the first is a king.
(ii) To win $\$ 1$ if the first is a king and the second is a queen.Which option is better? Or are they equivalent? Explain briefly.

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Key Concepts

Multiplication Rule in Probability

This rule is used to calculate the joint probability of two events occurring together. When events are dependent, the rule involves multiplying the probability of the first event by the conditional probability of the second event, adjusting for the fact that the events affect each other.

Conditional Probability

Conditional probability is the likelihood of an event occurring given that another event has already occurred. This is particularly important in sequential events, where the outcome of the first draw can affect the probability of subsequent draws.

Probability of a Single Event

This concept refers to calculating the likelihood that a specific event will occur by dividing the number of favorable outcomes by the total number of possible outcomes. In card games, this often involves determining the chance of drawing a particular type of card from a deck.

Joint Probability of Sequential Events

This concept involves finding the probability that two events happen in sequence. When events are not independent, such as drawing cards without replacement, the probability of the second event may depend on the outcome of the first.

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