Answer:
The probability that the students chosen are not both girls is 62/95 ⇒ (c)
Step-by-step explanation:
* Lets explain how to find the probability of an event
- The probability of an Event = Number of favorable outcomes ÷ Total
number of possible outcomes
- P(A) = n(E) ÷ n(S) , where
# P(A) means finding the probability of an event A
# n(E) means the number of favorable outcomes of an event
# n(S) means set of all possible outcomes of an event
- Probability of event not happened = 1 - P(A)
- P(A and B) = P(A) . P(B)
* Lets solve the problem
- There is a group of students
- There are 8 boys and 12 girls in the group
∴ There are 8 + 12 = 20 students in the group
- The students are sent to represent the school in a parade
- Two students are chosen at random
∴ P(S) = 20
- The students that chosen are not both girls
∴ The probability of not girls = 1 - P(girls)
∵ The were 20 students in the group
∵ The number of girls in the group was 12
∴ The probability of chosen a first girl = 12/20
∵ One girl was chosen, then the number of girls for the second
choice is less by 1 and the total also less by 1
∴ The were 19 students in the group
∵ The number of girls in the group was 11
∴ The probability of chosen a second girl = 11/19
- The probability of both girls is P(1st girle) . P(2nd girl)
∴ The probability of both girls = (12/20) × (11/19) = 33/95
- To find the probability of both not girls is 1 - P(both girls)
∴ P(not both girls) = 1 - (33/95) = 62/95
* The probability that the students chosen are not both girls is 62/95
