DQ2WEEK2 MAT-274.docx - Consider a standard deck of cards(52 with each of four suits – club diamond heart spade and drawing two cards What is the

# DQ2WEEK2 MAT-274.docx - Consider a standard deck of...

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Consider a standard deck of cards (52 with each of four suits – club, diamond, heart, spade) and drawing two cards. What is the probability of two hearts with replacement? Without replacement? With replacement P(Both are Hearts)= P(the First card is a Heart)*P(Second card is a Heart) P(the First card is a Heart)= 13/52 Since the card is being replaced there are still 13 hearts left in the deck, and still 52 total cards remaining. P(Second card is a Heart)=13/52 P(Both are Hearts) = 13/52*13*55 =169/2704 = 1/16 = .0625 or 6.25% Without replacement P(Both are Hearts)= P(the First card is a Heart)*P(Second card is a Heart) P(the First card is a Heart)= 13/52 There are 12 Hearts left in the deck if one is pulled and not replaced, and 51 total cards remaining. P(Second card is a Heart)=12/51 P(Both are Hearts) = 13/52*12*51 =156/2652 = 1/17 = .0588 or 5.88% The occurrence of some events may affect the probability of the occurrence of others. For example, the complementary events A and A cannot occur simultaneously. If one took place the other is out of the game: P(A|A) = 0.

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• Spring '18
• Probability theory, probability ​P, occurrence of some events

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