MATH SOLVE

4 months ago

Q:
# Two students from a group of eight boys and 12 girls are sent to represent the school in a parade.If the students are chosen at random, what is the probability that the students chosen are not both girls?a. 12/190b. 33/95c. 62/95d. 178/190

Accepted Solution

A:

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