Answer:
the probability you lose one or more friends is 0.9836
Step-by-step explanation:
Given the data in the question;
P( you lose one or more friend ) = 1 - P( keeping all friends )
Now, keeping all friends is possible only when each friend receives red candy.
As there are only 9 red candies and 9 friends, 1 red candy needs to be given to each friend out of 9 candies
Thus, total candies given = 63
and each friend will get 8 non red and 1 red candy
Thus, P( keeping all friends )
= [ ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ ] / × ⁶³C₉
SO
⁹C₁ = 9!/(1!(9-1)!) = 9 and ⁴⁹C₇ = 63!/(9!(63-9)!) = 23,667,689,815
so
P( keeping all friends ) = [ 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 ] / 23,667,689,815
P( keeping all friends ) = 387,420,489 / 23,667,689,815 = 0.016369
P( you lose one or more friend ) = 1 - P( keeping all friends )
P( you lose one or more friend ) = 1 - 0.016369
P( you lose one or more friend ) = 0.9836
Therefore, the probability you lose one or more friends is 0.9836
