Question

Blood group describes the type of blood a person has. It is a classification of blood based on the presence or absence of inherited antigenic substances on the surface of red blood cells. Blood types predict whether a serious reaction will occur in a blood transfusion. In a sample of 50 people, 21 had type O blood, 22 had type A, 5 had type B and the rest had type AB blood group.

Based on the above information, answer the following questions.

1. What is the probability that a person chosen at random had type O blood group?
2. What is the probability that a person chosen at random had type AB blood group?
3. What is the probability that a person chosen at random had neither type A nor type B blood group?
4. What is the probability that a person chosen at random had either type A or type B or type O blood group?

Answer 1

Given Data:

Total number of people: n(S) = 50

People with blood group (O): n(O) = 21

People with blood group (A): n(A) = 22

People with blood group (B): n(B) = 5

People with blood group (AB): n(AB) = 50 – (21 + 22 + 5) = 50 – 48 = 2

i. Probability that a person has type O blood group:

Formula: \[P(O) = \frac{n(O)}{n(S)}\]

Calculation: \[P(O) = \frac{21}{50}\]

ii. Probability that a person has type AB blood group:

Formula: \[P(AB) = \frac{n(AB)}{n(S)}\]

Calculation: \[P(AB) = \frac{2}{50} = \frac{1}{25}\]

iii. Probability that a person has neither type A nor type B blood group:

People having neither type A nor type B must have type O or type AB.

Number of favourable outcomes: \[n(\text{neither } A \text{ nor } B) = n(O) + n(AB) = 21 + 2 = 23\]

Calculation: \[P(\text{neither } A \text{ nor } B) = \frac{23}{50}\]

iv. Probability that a person has either type A or type B or type O blood group:

Number of favourable outcomes: \[n(A \text{ or } B \text{ or } O) = 22 + 5 + 21 = 48\]

Calculation: \[P(A \text{ or } B \text{ or } O) = \frac{48}{50} = \frac{24}{25}\]