Question 6: In this exercise, we consider a standard deck of 52 cards. We choose

Question

Question 6: In this exercise, we consider a standard deck of 52 cards. We choose, uniformly at random, one card from the deck. Define the events A "the rank of the chosen card is Ace", = B - the suit of the chosen card is dimonds Are the events A and B independent? As always, justify your answer. . Assume we remove the Queen of hearts from the deck. We choose, uniformly at random, one card from the remaining 51 cards. Define the events C- D- "the rank of the chosen card is Ace" "the suit of the chosen card is diamonds" Are the events C and D independent? Again, justify your answer

Explanation / Answer

No. of ACE in a deck = 4

P(A) = 4/52

No. of diamonds card is 13

P(B) = 13/52 = 1/4

No. of cards which are both diamond and an ace = 1

P( A intersection B ) = 1/52 = 1/4 * 4/52 = P(B) * P(A)

since, P (A interesection B) = P(A) * P(B) , therefore A and B are independed events

2.

No. of Ace in this modified deck = 4

P(C) = 4/51

P(D) = 13/51

P(C intersection D) = 1/51 which is not equal to P(C) *P(D)

Thus, C and D are not independent events

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.