Question

he following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? Yes. The events can 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 events cannot occur together. No. The probability of drawing a specific second card depends on the identity of the first card. (b) Find P(ace on 1st card and ten on 2nd). (Enter your answer as a fraction.) (c) Find P(ten on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a ten in either order. (Enter your answer as a fraction.)

Answer 1

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he following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.

EXPLANATION ::-

(a) Are the outcomes on the two cards independent? Why? Yes. The events can 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 events cannot occur together. No. The probability of drawing a specific second card depends on the identity of the first card

ANS ::-

(A) Are the outcomes on the two cards independent? Why?

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.Yes. The events can occur together.    No. The events cannot occur together.No. The probability of drawing a specific second card depends on the identity of the first card.

ANS ::-

No. The probability of drawing a specific second card depends on the identity of the first card.

This is because the cards are drawn without replacement. This would affect the probability of the second card.

(b) Find P(ace on 1st card and ten on 2nd). (Enter your answer as a fraction.)

ANS ::-

P(ace on 1st card and nine on 2nd).

There are a total of 4 aces and 4 nines.

When an ace is drawn then only 51 cards remains from which we have to draw a nine.

P(getting ace on first card) = 4/52

P(getting nine on second card) = 4/51

P(ace on 1st card and nine on 2nd) = (4/52) × (4/51) = 16/2652 = 4/663

(c) Find P(ten on 1st card and ace on 2nd). (Enter your answer as a fraction.)

ANS ::-

P(nine on 1st card and ace on 2nd)

When 9 is drawn it leaves 51 cards

P( getting 9 on first draw) = 4/52

P(nine on 1st card and ace on 2nd) = (4/52) × (4/51) = 4/663

(d) Find the probability of drawing an ace and a ten in either order. (Enter your answer as a fraction.)

ANS ::-

P( getting an ace and a nine)

We need to find probability of getting an ace and a nine.

This can happen in 2 ways.

Getting an ace in first draw and a nine in second draw or

Getting a nine in first draw and an ace in the second draw

P( getting an ace and a nine) =

P ( getting ace first and nine on second draw) + P( getting nine on first and ace on second draw)

= (4/52 × 4/51) + (4/52 × 4/51)

= (4/663) + (4/663)

= 8/663

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