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1.Suppose a box contains three cards, one with both sides white, one with both sides black, and one with one side white and the other side black. If you pick a card at random, and the side facing you is white, then the probability that the other side is white is 1/2.

2.A gardener throws 18 seeds onto an equilateral triangle shaped plot of land with sides of length one metre. Then at least two seeds are within a distance of 25 centimetres.

can anyone help to solve which of the above statements are true.thank you.

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What did you try? –  Did Sep 23 '12 at 18:34
    
Is this homework? Hints: 1) write down a sample space and model. 2) find the area of the triangle, and then approximate (exact will be difficult) the minimum area needed by 18 seeds separated as given. –  kjetil b halvorsen Sep 23 '12 at 18:41
    
i think problem 2 should not be called a probability problem. –  miracle173 Sep 23 '12 at 20:36

2 Answers 2

Hints:

1) is an exercise in Bayes's Theorem. Let $A_i$, $i=1,2,3$, be the events that you pick card number $i$, and $B$ the event that the side facing you is white. We have to assume that the side of the card you are looking at was also chosen randomly, independent of the card that was picked. You want the conditional probability $P(A_1 | B)$.

2) Divide up the plot into equilateral triangles of side $25$ centimetres. How many are there?

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No, 1) isśn really Bayes theorem, it is much more basic than that. Too many people like to refer to Bayes all the time! –  kjetil b halvorsen Sep 23 '12 at 18:42
    
Yes, you could find $P(B)$ by symmetry in this case, or just by counting the numbers of white and black sides. –  Robert Israel Sep 23 '12 at 18:47

1.for first question simply we know that if card's one side is white then there are only two options left WB and WW (W=white card , B=Black card) and BB is phased out Thus Conditional Probablity is 1/2

2.in this question you need to take copy and pen and solve it visually steps to solve are as follow

a)draw equalateral triangle of 100cm sides

b)as it is required every pt should be 25 cm away so we take circle of 12.5 (as seed cordinate is same as that of circle's cente) we take 18 circles

c)now place circle on three vertex of triangle so we lose 25 cm in each side

d)in each side we can again place 3 more circlesor radius 12.5 thus on boundry of triangle we seeded 3+(3+3+3) total 12 seeds

e)then we make an equalateral triangle with same incircle of length 50cm inside bigger one and again place those circles on the plot as we have done in steps(a to d)

f)now we can place 3 seeds(vertex) + 3 seeds on the edges=6

g)so we places 18 circle of radius 12.5 without overlapping each other thus

Statement 2) is False

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