Question

The daily amount of water drunk by an elephant in Serengeti National Park is evenly distributed between 0 and 60 liters. 1. What is the probability that an elephant drinks only 25 liters of water at during a day? 2. What is the probability that it will take 40 days for an elephant drink at least 45 liters of water for the first time? 3. What is the probability that it will take 11 days for an elephant drink at least 45 liters of water for the fifth time? 4. There is a certain parasite in these elephants. We have identified in average 35 of these parasites per elephant. What is the probability that we find more than 2 parasites on a randomly chosen elephant

Answer 1

in uniform distribution : [a,b]

P(q<=x<=r) = (r-q) / (b-a)

1.

P(drink only 25 litres of water)

= P(0<=x<=25)

= (25-0)/(60-0)

= 25/60

= 0.4167

2.

p(atleast 45 litre)

= P(45<=x<=60)

= (60-45)/(60-0)

= 0.25

P( it will take 40 days for an elephant drink at least 45 liters of water for the first time )

= P(less than 40 litre for 39 days) * P(atleast 45 litre on 40th day)

= (1-0.25)^39 * (0.25)

= 0.00000335219

3.

P(5th time on 11 th day)

= P(4 times in 10 days)*P( at least 45 liters on 11th day)

= [ 10C4 * (0.25^4) * (1-0.25)^6 ] * 0.25

= [210 * (0.25^4) * (1-0.25)^6 ] * 0.25

= 0.0365

4.

here, event/time = parasites/elephant = 35 parasites/elephant

P(more than 2 parasite in 1 elephant) = 1 - P(0) - P(1) - P(2)

= 1 - e^(-35*1) * (35*1)^0/(0!) - e^(-35*1) * (35*1)^1/(1!) - e^(-35*1) * (35*1)^2/(2!)

= 0.9999999999995911131781

≈ 1

(please UPVOTE)