Question

1. )A special deck of cards consists of  541 cards,  66 of which are red;  the rest are black. If a card is selected at random and you look at it and remember what it is or write it down, then you  replace it into the same deck, shuffle the deck at least 7 times, then select a card. 7 shuffles is an adequate number to thoroughly mix the cards and prevent any doubts,   Find the probability that both cards are red.  leave answer as an unreduced fraction

Answer 1

A special deck of cards consists of 541 cards, 66 of which are red & the rest are black.

A one card is selected at random observed it and put that card in same deck , shuffle the deck 7 time and again select the one card .

We here find out the probability that both the cards are red.

P ( both cards are red) = P ( First card is red)* P(second card is red)

There are 66 red cards in special deck of 541 cards. Therefore Probability of first card is red is:

P ( first card is red) =

After the first card selected and observed replace that card in same deck, shuffle the deck 7 time .Therefore in deck there are 66 red and again select the one card from special deck of 541 cards.The probability of the second card is also red is:

P( Second card is red)=

P ( both cards are red) = P ( First card is red)* P(second card is red)

P ( both cards are red) =  

P ( both cards are red)=0.01488

the probability that both the cards are red is 0.01488