Question 469398: Can someone please with this one.
A board game uses the deck of 20 cards shown. 4 rows of cards and they are from 1-5.
firt row - 1,2,3,4,5
second row - 1,2,3,4,5
thrid row - 1,2,3,4,5
fourth row - 1,2,3,4,5
Two cards are selected at random from this deck. Determine the probability of they both show even numbers
a) with replacement
b) without replacement
Answer by ccs2011(207)   (Show Source):
You can put this solution on YOUR website! Given 4 sets of {1,2,3,4,5}
Notice there are 3 odd (1,3,5) and 2 even (2,4)
Multiply by 4, which gives 12 odds and 8 evens in entire deck
So chance of picking an even number is 8/20= 2/5
With replacement:
Each selection is independent in this case, so probabilities remain constant
Probability of picking even on 1st card is 2/5
Probability of picking even on 2nd card is 2/5
Therefore probability of both cards being even is 4/25 or 0.16
Without replacement:
selections are not independent of each other, so probabilities may change
Probability of picking even on 1st card is 2/5
Now there is one less card in deck and one less even card
total = 19, even = 7, odd = 12
Probability of picking even on 2nd card is 7/19
Therefore probability of both cards being even is 14/95 or 0.147
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