Genetic disease

One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has 3 children. What is the probability of this family having one child who inherited this genetic disease?

Correct answer:

p =  0.4219

Step-by-step explanation:

$$\begin{gathered} C_1(3)=\left({\displaystyle \genfrac{}{}{0px}{}{3}{1}}\right)={\displaystyle \frac{3!}{1!(3-1)!}}={\displaystyle \frac{3}{1}}=3 \\ q=25\mathrm{\%}={\displaystyle \frac{25}{100}}=0.25 \\ n=3 \\ k=1 \\ p=\left(\genfrac{}{}{0px}{}{n}{k}\right)\cdot q^k\cdot (1-q{)}^{n-k}=3\cdot 0.25^1\cdot (1-0.25{)}^{3-1}=0.4219 \end{gathered}$$

Try another example

Related math problems and questions:

• Probability of malaria
  A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random (i) one is negative while the other tested positive? (i) both patient
• Family
  What is the probability that a family with 7 childrens have: exactly 6 dívek? 2 dívky and 5 boys? Consider the birth probability of a girl is 48.87% and boy 51.13%.
• Family
  94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
• Doctors
  The drug successfully treats 90% of cases. Calculate the probability that he will cure at least 18 patients out of 20?
• Seeds
  The germination of seeds of a certain species of carrot is 96%. What is the probability that at least 25 seeds out of 30 will germinate?
• Bernoulli distribution
  The production of solar cells produces 2% of defective cells. Assume the cells are independent and that a lot contains 800 cells. Approximate the probability that less than 20 cells are defective. (Answer to the nearest 3 decimals).
• Families 2
  Seven hundred twenty-nine families are having six children each. The probability of a girl is 1/3, and the probability of a boy is 2/3. Find the number of families having two girls and four boys.
• Binomial probability
  What is the binominal probability that at least 4 of the 6 trials (n=6) are succeeded where φ = 0.50?
• Covid-19
  Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents was infected.
• Records
  Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors?
• Sales
  From statistics of sales goods, item A buy 51% of people and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B?
• All use computer
  It is reported that 72% of working women use computers at work. Choose 3 women at random, find the probability that all 3 women use a computer in their jobs.
• Utopia Island
  The probability of disease A on the island of Utopia is 40%. The probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women o
• Internet anywhere
  In school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that a) exactly 5 have access to the internet. b) At least 6 students have access to the internet
• Alopecia
  Medical literature indicates that 45% of men suffer from alopecia. For random sample of 8 men, calculate the probability that: (a) exactly four men suffer from alopecia. (b) at most two men suffer from alopecia.
• Dice
  We throw five times the dice. What is the probability that six fits exactly twice?
• Left handed
  It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?