Answered

From beginner to expert, IDNLearn.com has answers for everyone. Join our knowledgeable community and get detailed, reliable answers to all your questions.

An experiment consists of ranomly drawing three cards in succession without replacement from a standard deck of 52 cards. Let A be the event of a king on the first draw, B the event of a king on the second draw, and C the even of a king on the third draw. Describe each of the events listed below and calculate its probability.

a. A ∩ B
b. A U B
c. A ∩ B ∩ C
d. A U B U C

Sagot :

Fichohidn

Answer:

0.0045248 ;

0.1312218 ;

0.0001809 ;

0.1659729

Step-by-step explanation:

Number of Kings in deck = 4

Total number of cards in deck = 52

Picking without replacement :

A = King on first draw :

P(A) = 4 / 52

A = King on 2nd draw :

P(B) = 3 / 51

A = King on 3rd draw :

P(C) = 2 / 50

1.) P(A n B) = P(A) * P(B)

P(A n B) = 4/52 * 3/51 = 12 / 2652 = 0.0045248

2.) P(A u B) = P(A) + P(B) - P(AnB)

P(AuB) = 4/52 + 3/51 - 0.0045248 = 0.1312218

3.) P(A ∩ B ∩ C) = P(A) * P(B) * P(C)

P(A ∩ B ∩ C) = 4/52 * 3/51 * 2/50 = 0.0001809

4.) P(A U B U C) =

P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) - P(AnBnC)

P(AnC) = P(A) * P(C) = 4/52 * 2/50 = 0.0030769

P(BnC) = P(B) * P(C) = 3/51 * 2/50 = 0.0023529

4/52 + 3/51 + 2/50 - 0.0045248 - 0.0030769 - 0.0023529 + 0.0001809 = 0.1659729

Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.