Suppose you are planning to study a species of squid at a local wildlife preserve, but out of the 34 locations for which they could be located, only 14 of them contain the species. Due to time constraints, you randomly select 5 locations. What is the probability that 3 of those contain squid and the remaining 2 locations do not contain squid?
X : Number of locations contain squid
n : Number locations selected = 5
Number of locations for which squid could be located = 34
Number of locations contain squid = 14
Probability that randomly selected location contain squid : p = 14/34 = 7/17
q = 1-p = 1-7/17 = 10/17
X follows a Binomial distribution ;
The probability mass function of X :
Probability that 'r' of the selected 5 locations (and remaining 5-r locations do not contain squid) is given by
probability that 3 of those contain squid and the remaining 2 locations do not contain squid = P(X=3)
probability that 3 of those contain squid and the remaining 2 locations do not contain squid = 0.2416
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