In austria, 30% of the population has a blood type of o+, 33% has a+, 12% has b+, 6% has ab+, 7% has o-, 8% has a-, 3% has b-, and 1% has ab-. if 15 austrian citizens are chosen at random, what is the probability that 3 have a blood type of o+, 2 have a+, 3 have b+, 2 have ab+, 1 has o-, 2 have a-, 1 has b-, and 1 has ab-?

The probability that 3 have a blood type of O+, 2 have A+, 3 have B+, 2 have AB+, 1 has O-, 2 have A-, 1 has B-, and 1 has AB- is 0.0011%

Explanation: For calculate the probability, we have to use multinomial distribution:

P=n!

n: number of trials, p: probability for each possible outcome, k: number of possible outcomes.

The probability of each blood type are:

If 15 Austrian citizens are chosen at random, there are 15 trials. n=15

for n1=3 because 3 P(0+)

for n2=2 because 2 P(A+)

for n3=3 because 3 P(B+)

for n4=2 because 2 P(AB+)

for n5=1 because 1 P(0-)

for n6=2 because 2 P(A-)

for n7=1 because 1 P(B-)

for n8=1 because 1 P(AB-)

k=8 (because there are 8 possibilities)

P=0.000011

Px100=0.0011