Question

4. An English-speaking tourist visits a country in which 30% of the population speaks English. He needs to ask someone directions. a) Find the probability that the first person he encounters will be able to speak English. b) The tourist sees four local people standing at a bus stop. Find the probability that at least one of them will be able to speak English.

Answer 1

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%