Pregunta

If you draw a card from a deck and do not replace it, what type of events does this represent when drawing a second card?

Ask by Herrera Edwards. in South Africa
Jan 24,2025

Solución de tutoría real

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Drawing a second card after the first without replacement represents dependent events because the first draw affects the probabilities of the second draw.

Solución

When you draw a card from a deck and do not replace it, the events that occur when drawing a second card represent dependent events. Here's the reasoning: 1. **Dependent Events**: In probability, two events are considered dependent if the outcome or occurrence of the first event affects the outcome or occurrence of the second event. In this case, drawing the first card changes the composition of the deck (there is one less card), which directly affects the probabilities associated with drawing the second card. 2. **Example**: - If you draw an Ace from a standard 52-card deck, there are now only 51 cards left in the deck. The probability of drawing another Ace on the second draw is now different than it was before the first draw because there is one less Ace in the deck (if the first card drawn was an Ace). In summary, drawing a second card after the first without replacement represents dependent events because the outcome of the first draw influences the probabilities of the second draw.

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Bonus Knowledge

When you draw a card from a deck and don’t replace it, this creates what's known as dependent events. This means that the outcome of your second draw is influenced by the first draw; the total number of cards and the composition of the deck has changed. For example, if you draw a heart first, there are now fewer hearts and fewer cards overall in the deck when you go to draw a second card. When approaching this scenario, keep in mind the reduced probabilities! Since you’re not replacing the first card, the odds shift with each draw. For instance, if you had a 1 in 52 chance of drawing an Ace initially, after one card is drawn, you’d have a 1 in 51 chance for the next one (assuming no Aces were drawn). Understanding this concept can help sharpen your skills in probability and card games alike!

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