Question

Emma plays card games. She picks a card at random from a well-suffled deck of $52$ cards. Then without putting the first card back, she picks a second card at random. Which type of compound event is this?

• A. Independent
• B. Dependent
• C. Simple
• D. None of the above

Answer 1

The correct option is B Dependent

$\underset{–}{\text{Compound Events}}$
Events that consist of two or more single events

Here, Emma picks first card, and without replacing the first one, she again picks the second card. Hence, this event is compound event as it consists of the following two single events:
$\bullet$ Event 1: Picking first card
$\bullet$ Event 2: picking second card without replacing the first card

$\underset{–}{\text{Dependent Events}}$
Compound events in which the outcome of one depends upon the outcome of the other

It is clear that as Emma is not replacing first card after pick-up, the chance of getting any card in event 2 absolutely depends on the outcome of event 1.

Hence, the compound event of sequential picking of two cards without replacement by Emma is a $\text{dependent event}$.