Answer:
Probability that two or more of them have Type A blood is 0.6242.
Step-by-step explanation:
We are given the approximate probabilities that a person will have blood type O, A, B, or AB.
Blood Type O A B AB
Probability 0.4 0.2 0.32 0.08
A group of 10 people are chosen randomly.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 10 people
r = number of success = two or more have Type A blood
p = probability of success which in our question is probability
that a person has Type A Blood, i.e; p = 20% or 0.20
LET X = Number of person having Type A Blood
So, it means X ~ Binom(n = 10, p = 0.20)
Now, Probability that two or more of them have Type A blood is given by = P(X [tex]\geq[/tex] 2)
P(X [tex]\geq[/tex] 2) = 1 - P(X = 0) - P(X = 1)
= [tex]1- \binom{10}{0}\times 0.20^{0} \times (1-0.20)^{10-0}-\binom{10}{1}\times 0.20^{1} \times (1-0.20)^{10-1}[/tex]
= [tex]1- 1 \times 1 \times 0.80^{10}-10 \times 0.20 \times 0.80^{9}[/tex]
= 0.6242
Hence, the probability that two or more of them have Type A blood is 0.6242.
