**Transcription:**A young child is trying his hand as a magician. He approaches you and says, "Pick a card, any card." You pick a card and look at it. Then you put it back in the deck which is then shuffled. You repeat this process 3 times. Then the budding magician tries to guess the three cards you selected.**What is the most likely outcome?**- ( ) Ace of hearts, Ace of clubs, Ace of diamonds- ( ) Ace of spades, Ace of clubs, Ace of spades- ( ) Ace of hearts, Ace of hearts, Ace of hearts- ( ) All of these outcomes are equally likely.- ( ) Ace of hearts, Ace of diamonds, Ace of hearts

Introduction: It is required to choose the correct option.Calculation: Assume that the game is being played using a standard deck of 52 cards, where each card is unique. Three card selections have to be made. The first card can be any of the 52 cards, with probability 152. This card is returned to the deck and the cards shuffled before picking the second card, so that the second card can be any of the 52 cards, with probability 152. The second card is also returned to the deck and the cards shuffled before picking the third card, so that the third card can also be any of the 52 cards, with probability 152. Therefore, any three selections will have probability 1523=1140608. Further note that, since every card selected is returned to the deck before selecting the next card, the selections are all independent of each other, and no selection ins influence by the previous selections. The first, second, third, and fifth options are, thus, all equally likely to occur, with the above probability. Hence, the correct option is, "All of these outcomes are equally likely"; the fourth option is correct.