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There are 13 hearts in a full deck of 52 cards. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws it took before the person picked a heart and, thereby, won. What is the probability that one will pick the first heart on the third draw or later?

Respuesta :

Answer:

9/16

Step-by-step explanation:

When the heart is picked in the third draw or later it is the favorite case.

When the heart is picked in either first draw or in second draw it is the unfavorite case.

Probability = favorable outcome /total outcome

Probability = 1 - (unfavorable outcome /total outcome)

Unfavorable case 1

Probability of heart picked in first draw = 13/52 = 1/4

Unfavorable case 2

Probability of heart picjec in second draw (I. e first draw is not heart) = 39/52 * 13/52

= 3/4*1/4

= 3/16

Total unfavorable probability = 1/4 + 3/16

= 7/16

Favorable probability = 1 - 7/16

= 9/16

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