What is the probability of drawing 2 cards at random which are all aces of the first card is placed back in the deck before the second card is drawn?
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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. Show
You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (b) Find P(ace on 1st card and nine on 2nd). (Enter your answer as a fraction.) (c) Find P(nine on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a nine in either order. (Enter your answer as a fraction.) Answer & Explanation Solved by verified expert (a) No. The probability of drawing a specific second card depends on the identity of the first card. (b) P=6634 (c) P=6634 (d) P=6634 Step-by-step explanation (a) 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 nine on 2nd). (Enter your answer as a fraction.) P=524×514=6634 4/52 is the probability of getting ace on the 1st draw 4/51 is the probability of getting nine on the 2nd draw The operation will be multiplication since and was used in the problem. You need to subtract the 1 to the overall number of cards since you draw one. It will be a different case if you return the card before drawing the second one. (c) Find P(nine on 1st card and ace on 2nd). (Enter your answer as a fraction.) P=524×514=6634 4/52 is the probability of getting nine on the 1st draw 4/51 is the probability of getting aceon the 2nd draw It is the same with problem (b). (d) The same process from the (b) and (c). Either way, it is the same since the number of ace and nine cards are the same which is 4 cards. What is the probability of drawing 2 aces from a deck of cards?The chance of drawing one of the four aces from a standard deck of 52 cards is 4/52; but the chance of drawing a second ace is only 3/51, because after we drew the first ace, there were only three aces among the remaining 51 cards. Thus, the chance of drawing an ace on each of two draws is 4/52 × 3/51, or 1/221.
What is the probability of drawing 2 aces given that we know one of the cards is an ace?(4∗3)/(4∗106)=3/106 is the probability of two aces when you get at least one ace.
What is the probability that both cards are aces if you replace the first card before drawing the second?The probability that both are aces is. = 1/ 221.
What is the probability of drawing 2 aces from a standard deck of cards given that the first card is on the cards are not to return to the deck?Correct answer:
Thus, for the first ace, there is a 4/52 probability and for the second there is a 3/51 probability. The probability of drawing both aces without replacement is thus 4/52*3/51, or approximately . 005.
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