Question

In a large population, 57 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?

Answer 1

Answer:

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1)  = 0.920493

Step-by-step explanation:

Step(i):-

Given  57 % of the people have been vaccinated

p = 57% =0.57

q = 1-p =1-0.57 = 0.43

n = 3

$P(X=r) = n_{C_{r} } p^{r} q^{n-r}$

Step(ii):-

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1) = P( x =1) + P(x =2)+P(x=3)             $P(X\geq 1) = 3_{C_{1} } (0.57)^{1} (0.43)^{3-1} + 3_{C_{2} } (0.57)^{2} (0.43)^{3-2} + 3_{C_{3} } (0.57)^{3} (0.43)^{3-3}$

$P(X\geq 1) = 3 (0.57) (0.43)^{2} + 3 (0.57)^{2} (0.43) + 1 (0.57)^{3} (0.43)^{0}$

               =  0.316179 + 0.419121 +0.185193

            = 0.920493

Final answer:-

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1)  = 0.920493

Answer 2

Answer:0.92

Step-by-step explanation:

Given

$57\%$ of Population is vaccinated

So, Probability of a person being vaccinated is $P=0.57$

and simultaneously , probability of not vaccinated is $1-P$

$=1-0.57=0.43$

Now, Probability that atleast one of them has been vaccinated is given by

$=1-P(\text{None of them is vaccinated})$

$=1-0.43\times 0.43\times 0.43$

$=1-0.0795$

$=0.92$