Answer:
a) 30%
b) 75.99%
Step-by-step explanation:
a) The probability that one random person will be able to speak English is equal to the percent of the population that speaks English. This is because, in the country, (number of favorable outcomes)/(number of total outcomes) = 30% = 0.3 = 3/10
b) The probability that at least one person speaks English is equal to 1 - (probability that none of them speak English). Of the 4 people, if N represents them not speaking English and Y represents them speaking English, here are a few possiblities:
NNNN
NYYY
NNYY
NNNY
YNNN
and so on. However, there is only one possibility where none of them speak English, and the opposite of "none" is "at least one". So, the probability thsat none of them speak English is P(A and B and C and D) = P(A)*P(B)*P(C)*P(D), where P(A) represents the probability that the first person doesn't speak English and so on. The probability that the first person doesn't speak English = 1 - (probability that the first person speaks English) = 1 - 30% = 0.7. Therefore, the probability that all of them don't speak English is 0.7^4 = 0.2401 and the probability that at least 1 of them speak English is 1- 0.2401 .= 0.7599 = 75.99%
