Hi! I could really use some help going through this problem step by step, I gave
ID: 3276137 • Letter: H
Question
Hi! I could really use some help going through this problem step by step, I gave it a start but get confused on following it all the way through!
Thank you in advance!
3.28 There are 52 cards in a deck of cards, 13 of which are hearts. Suppose you randomly select 2 cards without replacement. Let Hi denote the event that a heart is obtained on the first draw, and let H2 denote the event that a heart is obtained on the second draw. (a) Use the law of total probability to find the probability you obtain a heart on the second draw, i.e. find P(H2). (b) Find the probability both cards are hearts, i.e. find P(H1 and H2) (c) Find the probability that a heart is obtained on the first draw or second draw, i.e. find P(H1 or H2). (d) What is the probability that a heart was obtained on the first draw given that a heart is obtained on the second draw? In other words, find P(H|H2).Explanation / Answer
(a) There are 52 cards and out of them there are 13 hearts
=> Probability that a heart is obtained on the first draw = 13/52
Probability that a heart is not obtained on the first draw = 39/52
Probability that a heart is obtained on the second draw if a heart is obtained on the first draw = 12/51
Probability that a heart is obtained on the second draw if a heart is not obtained on the first draw = 13/51
=> Probability that a heart is obtained on the second draw P(H2) = 13/52 * 12/51 + 39/52 * 13/51 = 0.25
(b) The probability that both are hearts P(H1 H2) = 13/52 * 12/51 = 0.0588
(c) P(H1 U H2) = P(H1) + P(H2) - P(H1 H2)
= 13/52 + 0.25 - 0.0588
= 0.4412
(d) P(H1|H2) = P(H1 H2) / P(H2)
= 0.0588 / 0.25
= 0.2353
This can also be done in another way. Since H2 would a heart, there are 12 hearts out of 51 for H1 and so the probability would be 12/51 or 0.2353.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.