Classify the events as dependent or independent. the events of getting two aces when two cards are drawn from a deck of playing cards and the first card is not replaced before the second card is drawn.

The events are dependent.

When the first card is not replaced, you change the probability of the second card. At the very least, you have changed the total number of cards to draw from.

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AFOKE88 AFOKE88 · Answer 2 · 2021-10-19T13:17:08+02:00

The classification of the 2 events as dependent or independent is that;

Event of the first card being an ace is independent while the event of drawing the second card is dependent.

Dependent events are simply those events whose outcome are affected by the probability of another event happening. In contrast, independent events are those that their outcomes are not affected nor influenced by the probability of other events happening.

We are given the event;

Getting two aces when two cards are drawn from a deck of playing cards and the first card is not replaced before the second card is drawn.

Now, when the first card is drawn from the deck of playing cards, it is not dependent on the probability of another event happening because it is the first card and thus, the event of the first card being an ace is independent.

However, after the first card is drawn, it is not replaced and this means that the number of cards in the deck has reduced by 1 and also the number of aces in the deck has reduced by 1. This means the probability of the second card drawn being an ace is not going to be the same as the first one drawn because it is dependent on the first one being drawn.

Thus, we can say the event of drawing the first card being an ace is independent while the event of drawing the second one being an ace is dependent.

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