1. (20) Rawdon\'s Leech Farms has a bucket of 1020 leeches, of which 627 are fem
ID: 3309761 • Letter: 1
Question
1. (20) Rawdon's Leech Farms has a bucket of 1020 leeches, of which 627 are female leeches and 393 are male leeches. If 50 leeches are chosen at random from the bucket, what 1s the probability that this group will be made up of (a) exactly 25 males and 25 females? (b) two or more females? (20) In the Rawdonville Lottery, five balls are chosen from an urn (without replacement) with the balls labeled 1 through 40. There is also a Slammin' Sammy ball which is chosen from a separate urn with balls labeled 1 through 13. You decide to play the lottery because it sounds like so much fun. So you choose five numbers between 1 and 40 and a Slammin' Sammy number , between 1 and 13. (a) What is the probability of winning the Rawdonville Lottery (that is, getting all five numbers to match the draw and matching the Slammin' Sammy ball)? (b) What is the probability of having three of your five choices natch the lottery draw wihile missing the Slammin' Sammy number?Explanation / Answer
Q1.
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
p = 627/1020 = 0.61471
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 50 * 0.61471
= 30.7355
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 50 * 0.61471 * 0.38529
= 11.8421
III.
standard deviation = sqrt( variance ) = sqrt(11.8421)
=3.4412
a.
P( X = 25 ) = ( 50 25 ) * ( 0.61471^25) * ( 1 - 0.61471 )^25
= 0.0291
b.
P( X < 2) = P(X=1) + P(X=0)
= ( 50 1 ) * 0.61471^1 * ( 1- 0.61471 ) ^49 + ( 50 0 ) * 0.61471^0 * ( 1- 0.61471 ) ^50
= 0
P( X > = 2 ) = 1 - P( X < 2) = 1
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