Consider a card deck consisting of 52 cards with 26 black and 26 red cards. Supp

Question

Consider a card deck consisting of 52 cards with 26 black and 26 red cards. Suppose that the cards are taken from the deck one by one and are uncovered. a) Calculate the probability that the third red card occurs at the trial i = 3, 4..., under the assumptions that each card is returned to a random location (put the card into the deck and shuffle). b) Calculate the probability that the third red card occurs at the trial i = 3, 4... under the assumptions that each card is not returned to the deck but is put aside.

Explanation / Answer

probability of getting red card is 26/52=1/2

a) already in first attempt and second we got red cards...

find probability that getting third red in third attempt is =26/52( beacuse card is returned deck and suffled...)

same as... 4 th 5th 6th attempts... =1/2 because cards were returned to deck

b)as per question ,already in first attempt and second we got red cards...

cards are not returned to deck

that means we have 24 red cards and 26 black cards

therfore, getting third red in third attempt is =24/50 =0.48

if didt get red card , that means we got black card

in that case we have 24 red and 25 black total 49

therofore ,getting third red in 4th attempt is = 24/49=0.489795

similary in 5th attempt=24/48=0.5

in i^th attempt =24/52+1-i

i=1,2,3,4,5,6.....

for just known,

at 29th attempt we have probability of 1 , if we didt get 3rd red card in last attempts

  

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