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This is a question from the Edexcel 2002 GCSE Calculator Paper and it has got me quite confused.
There are n beads in a bag.
6 beads are black and all the rest are white.
Heather picks one bead at random from the bag and does not replace it.
She picks a second bead at random from the bag.
The probability that she will pick 2 white beads is 0.5.
Show that n²-25n+84=0
Any idea how to solve it??
I've worked out that 6/n are black and (n-6)/n are white.
Therefore with a tree diagram
1st Pick
6/n - Black
(n-6)/n - White
2nd Pick
5/(n-1)Black (after a black has been picked)
(n-6)/(n-1)White (after a black has been picked)
6/(n-1)Black (after a white has been picked)
(n-6)/(n-1)White (after a white has been picked)
And I believe that:
(n-6)²/n*(n-1)=0.5
But after that, I'm lost.
Nearly all correct so far, but the second probability for white should be (n-7)/(n-1), because one white has already been removed. So you have (n-6)(n-7)/n(n-1) = 0.5.
From there you just manipulate your equation to get it into standard quadratic form.
(n-6)(n-7)/n(n-1)=0.5
(n-6)(n-7) = 0.5n(n-1)
n²-13n+42 = 0.5n²-0.5n
0.5n² - 12.5n + 42 = 0
n² - 25n + 84 = 0
Why did the vector cross the road?
It wanted to be normal.
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