Persons entering a blood bank are such that 1 in 9 have type O+ blood

gamau6v

gamau6v

Answered question

2021-11-26

Persons entering a blood bank are such that 1 in 9 have type O+ blood and 1 in 30 have type O- blood. Consider six randomly selected donors for the blood bank. Let X denote the number of donors with type O+ blood and Y denote the number with type O- blood. Find the probability distributions for X and Y. Also find the probability distribution for X+Y, the number of donors who have type O blood.

Answer & Explanation

Stephanie Mann

Stephanie Mann

Beginner2021-11-27Added 25 answers

Step 1
There are 6 donors in a blood bank
1 in 9 have type O+ blood and 1 in 30 have type O- blood.
Step 2
Let X denote the number of donors with O+ blood
n=Number of donors=6
p=probability that the donor has O+ blood=19
q=1p=89
Let us assume that having O+ blood is a success then X denote number of successes in n trials
Therefore, X follows Binomial distribution with parameters n=6 and p=19
The probability mass function of Binomial distribution is P(X=x)=ncxpxqnx,x=0,1,2,3,4,5,6
Step 3
Let Y denote the number of donors with O- blood
n=Number of donors=6
p=probability that the donor has O- blood=130
q=1p=2930
Let us assume that having O- blood is a success then Y denote number of successes in n trials
Therefore, Y follows Binomial distribution with parameters n=6 and p=130
The probability mass function of Binomial distribution is P(Y=y)=ncypyqny,y=0,1,2,3,4,5,6
Step 4
Let X+Y denote the number of donors who have blood type O
n=Number of donors=6
p=probability that the donor has O blood
=P(The donor has O+)+P(The donor has O-)
=19+130
=1390
q=1p=7790
Let us assume that having O blood is a success then X+Y denote number of successes in n trials
Therefore, X+Y follows Binomial distribution with parameters n=6 and p=1390
The probability mass function of Binomial distribution is P(X+Y=r)=ncrprqnr,r=0,1,2,3,4,5,6

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