1. A pond contains 5 red fishes and 3 blue fishes. A fisherman caught 6 fishes.
ID: 3173987 • Letter: 1
Question
1. A pond contains 5 red fishes and 3 blue fishes. A fisherman caught 6 fishes. Which is more probable, that the fisherman caught 3 red fish or 4 red fish?
2. An urn contains two red balls and two blue balls. A round of experiment consist of randomly picking a ball and replacing it with a blue ball. The experiment stops when the urn has all blue balls. What is the probability that the experiment will end before the round 4, i.e., in the round two or three?
3.(part 1) A Bernoulli experiment has a probability of success of 0.2. What is the probability that the five repeats of the experiment yield two successes?
(Part 2)In a recently acquired batch of markers we have 15% of defective ones. We randomly pick markers from the batch. What is the probability that the first two defective markers picked were fifth and sixth?
Explanation / Answer
1) Pond has 5 red ones and 3 green ones
Probability of fisher man catching 3 red = 5C3* 3C3 / 8C6 = 10* 1/23 = 10/23
Probability of catching 4 red = 5C4 * 3C2 / 8C6 = 5*3/8C6 = 15/23
Probability of catching 4 red > probability of catching 3 red fishes
2) Urn have 2 red and two blue
Experiment end at round two, i.e probability of taking 2 balls red with replacement
= 1/2 * 1/4 = 1/8
Experiment end at round three, i.e probability of taking 2 balls red and one blue with replacement
red,blue,red = 1/2 * 3/4 * 1/4 = 3/32
blue, red, red = 1/2 * 1/2 * 1/4 = 1/32
TOTAL = 3/32 + 1/32 + 1/8 = 1/4
3) GIven probability of success = p = 0.2
The probability that the five repeats of the experiment yield two successes
p(X=2)
nCr * p^r*q^(n-r)
= 5C2 * 0.2^2 * 0.8^3
= 0.02048*10
= 0.2048
_______________________________
Given 15% are defective ones
p = 0.15
defectives picked are 5th and 6th
= q*q*q*q*p*p
= 0.85^4*0.15^2
= 0.01174
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