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There are 8 sweets in a box. There are n jelly beans and the rest are cola bottles. Colin takes 2 sweets out of the box at random. Write an expression for the probability of getting 2 cola bottles. Give your expression as a single fraction and simplify fully.

Sagot :

Answer:

Probability expression = 1 - n/7 - n/8 + n^2 / 56

Probability single fraction based on example = 3/28

Step-by-step explanation:

Total sweets = 8. n jelly beans , 8 - n cola bottles

Prob (getting 1st cola bottle) = Cola bottles / Total sweets = (8-n) /8

Prob (getting 2nd cola bottle) = remaining cola bottles / remaining total sweets = (8 - n - 1) / (8-1) = (7-n) / (7)  

Prob (getting both 1st & 2nd cola bottle) = [ (8-n) /8 ] x [ (7-n) / 7 ]

(1 - n/8) x (1-n/7) = 1 - n/7 - n/8 + n^2 / 56

Eg : 5 jelly beans , 3 cola bottles

Similarly, Prob (2 cola bottles) = 3/8 x 2/7 = 6 / 56 = 3/28

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