Answer :
The probability that exactly two will have this mild side effect is
[tex]P(X=2)=0.1229[/tex]
Probability is defined as the likelihood that a trial will succeed or fail. The ratio of positive events to all possible outcomes is known as probability. The probability scale ranges from 0 to 1.
Given data:
The probability of all patients that will have the mild side effect is p=5%=0.05
The number of people selected is n=14
The expression for the probability that exactly two will have this mild side effect is given as,
[tex]P(X=x)=^{n}C _{x} p^{x} (1-p)^{n-x}[/tex]
Substituting the values in the above equation as
[tex]P(X=x)=^{n}C _{x} p^{x} (1-p)^{n-x}\\P(X=2)=^{14}C _{2} 0.05^{2} (1-0.05)^{14-2}\\P(X=2)=91*0.0025*0.54036\\P(X=2)=0.1229[/tex]
Thus the probability that exactly two will have this mild side effect is
[tex]P(X=2)=0.1229[/tex]
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