A teacher needs to find out how many seventh graders will be going on a field trip. Which best describes the population that the
2 answers:
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Answer: Part a)
part b)
Step-by-step explanation:
The probability is calculated as follows:
We have proability of any event E =
For part a)
Probability that a red ball is drawn in first attempt =
Probability that a red ball is drawn in second attempt=
Probability that a red ball is drawn in third attempt =
Generalising this result
Probability that a red ball is drawn in [tex}i^{th}[/tex] attempt =
Thus the probability that events occur in succession is
Thus =
Thus our probability becomes
Part b)
The event " r red balls are drawn before 2 whites are drawn" can happen in 2 ways
1) 'r' red balls are drawn before 2 white balls are drawn with probability same as calculated for part a.
2) exactly 1 white ball is drawn in between 'r' draws then a red ball again at draw
We have to calculate probability of part 2 as we have already calculated probability of part 1.
For part 2 we have to figure out how many ways are there to draw a white ball among (r) red balls which is obtained by permutations of 1 white ball among (r) red balls which equals
Thus the probability becomes
Thus required probability of case b becomes
=