Fill in the blanks for Q1, Q2, Q3 and choose one between A to C for Q4 Problem 1

Question

Fill in the blanks for Q1, Q2, Q3 and choose one between A to C for Q4

Problem 1 The chance that the top card in a well shuffed deck is a heart or a diamond is (Q1) The chance that the fourth card from the top of the deck is a face card is (Q2) The chance that the top card in the deck is a heart or a diamond given that the fourth card from the top is a face card is (Q3) Are the events that the top card is a heart or a diamond and that the fourth card is a face card independent? (Q4) A: no B: cannot be determined without knowing other cards C: yes

Explanation / Answer

Q1) P(top card is a heart or a diamond) = 26/52 = 0.5

Q2) P(forth card from top is a face card) = (4x3)/52

= 3/13

= 0.2308

Q3) P(top card is a heart or a diamond | forth card from top is a face card) = P(top card is a heart or a diamond and forth card from top is a face card)/P(forth card from top is a face card)

= (1/2)(3/13)/(3/13)

= 0.5

Q4) C: Yes

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