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You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. (a) Are the outcomes on the two cards independent? Why? Yes. The events can occur together. No. The events cannot occur together. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. No. The probability of drawing a specific second card depends on the identity of the first card. Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (b) Find P(ace on 1st card and king on 2nd). (Enter your answer as a fraction.) Incorrect: Your answer is incorrect. (c) Find P(king on 1st card and ace on 2nd). (Enter your answer as a fraction.) 4/663 Incorrect: Your answer is incorrect. (d) Find the probability of drawing an ace and a king in either order. (Enter your answer as a fraction.)

Respuesta :

Answer:

(a) Yes, the outcomes on the two cards independent.

Because, both events cannot occur together.

(b) P(ace on 1st card and king on 2nd) = [tex]\frac{4}{52}\times \frac{4}{52} = \frac{1}{169}[/tex]

(c) P(king on 1st card and ace on 2nd) = [tex]\frac{4}{52}\times \frac{4}{52} = \frac{1}{169}[/tex]

(d) The probability of drawing an ace and a king in either order =

P(ace on 1st card and king on 2nd) + P(king on 1st card and ace on 2nd)

[tex]= \frac{1}{13}+\frac{1}{13} = \frac{2}{13}[/tex]

The following probabilities are;

  • Yes, the outcome of the two-card is independent, because both events cannot occur together.
  • The Probability of ace on the 1st card and king on the 2nd card is 1/169.
  • The Probability of king on the 1st card and ace on the 2nd is 1/169.
  • The probability of drawing an ace and a king in either order is 2/13

What is probability?

Probability means possibility. It deals with the occurrence of a random event. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

It is given that you draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck.

Then

a.  Yes, the outcome of the two-card is independent, because both events cannot occur together.

b.  The Probability of ace on the 1st card and king on the 2nd card.

[tex]\rm P(Ace, \ King ) = \dfrac{4}{52} * \dfrac{4}{52}\\\\P(Ace, \ King ) = \dfrac{1}{169}[/tex]

c.  The Probability of king on 1st card and ace on 2nd.

[tex]\rm P(King, \ Ace ) = \dfrac{4}{52} * \dfrac{4}{52}\\\\P(King, \ Ace) = \dfrac{1}{169}[/tex]

d.  The probability of drawing an ace and a king in either order.

[tex]\rm P(King or \ Ace ) = \dfrac{4}{52} + \dfrac{4}{52}\\\\P(King \ or \ Ace) = \dfrac{2}{13}[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

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