Question

Problem 6 A lake contains 600 fish, eighty (80) of which have been tagged by scientists. A researcher randomly catches 15 fish from the lake. a. Find a formula for the probability mass function of X, the number of fish in the researcher's sample, which are tagged b. Find the probability that none of the fish he catches are tagged c. What is the number of tagged fish he expects to catch?

Answer 1

Solution 6 :- No, no. of fishes in lake = 600 no. of fishes been tagged = 80 probability of fishes been tagged I no. of fishes tagged . no. of fishes in lake = = = 0,133

(a) x = no. of fishes tagged in e sample of 15 since x is binomial , P(x=) - "C. (63' (1-1) 5-7 So going same way for n=15, probability mas function for getting & fishes is = 15 (p)*(1-P) - " (0,33) (0,867)\5-* 15-X

none (6) probability of none of the catched fishes are tagged - mean p(2=0) ? = P(x=0) = 'CO (0.133) (0,867)"} = (0,867) = 0.1176 so propability that none of fishes are tagged out of is catched is equal to 10. 1176 ]

(c) catched no. of fishes = 15 =n Pacobability of tagged fishes (Þ) = 0,133 Expected value of binomial & = np - fishes Expected no. of tagged been caught = np = 0.133 x 15 = 1.995 > 2 fishes are expected to be tagged.