The following data represents the language spoken at home by age for residents i

ID: 3180924 • Letter: T

Question

The following data represents the language spoken at home by age for residents in San Francisco between the age of 5 and 64 years. (a) Compute the probability that a randomly selected resident who speaks Spanish at home is 5-17 years old. (b) Compute the probability that a randomly selected resident is 18-64 years old, given that they speak English only? (c) Compute the probability that a randomly selected resident who is 5-17 years old speaks Spanish at home. (d) Compute the probability that a randomly selected resident speaks some Asian/Pacific Islander language if we know that the person is 5-17 years old.

Explanation / Answer

et’s calculate the total population of each category first:

5-17

18-64

Total

English

34903

312627

347530

Spanish

15620

61301

76921

OtherIndoEuro

4170

33258

37428

Asian

24861

129927

154788

Other

1499

5537

7036

total

81053

542650

623703

These are the cases of conditional probabilities. Means, given the probability of B, what is the probability of A:

For such cases, Bayes Theorem says:

P(A|B) = P(A and B)/P(B)

A) P(5-17| Spanish)

= P(Number of 5-17 year old resident and speaks Spanish) / P(Spanish)

=(15620 / 623703) / (76921/623703)

Answer = 0.203065483

B) P(18-64|English):

=P(Number of 18-64 year old resident and speaks English) / P(English)

=(312627 / 623703) / (347530 / 623703)

Answer = 0.899568383

C) P(Spanish|5-17)

= P(Number of 5-17 year old resident and speaks Spanish) / P(5-17 year old)

=(15620 / 623703) / (81053/623703)

Answer = 0.192713

D) P(Asian/Pacific Islander language | 5-17 years old)

=P(Number of 5-17 years old Asian/Pacific Islander language speaking) / P(5-17 year old)

= (24861/623703) / (81053/623703)

Answer = 0.129954482