simple stats questions

• Sep 3rd 2009, 02:45 AM
wik_chick88
simple stats questions
hey everyone!! have a few questions that are for an economics subject but are basic stats stuff, and ive done them i just wanted someone to check if i have the right/wrong answer and help me if i have the wrong answer? thanks in advance!!

QUESTION ONE
Suppose that the probability that tomorrow will be rainy is 0.38 and the probability of it being windy tomorrow is 0.31. Also the probability that it will rain and be windy tomorrow is 0.09. What is the probability it will be windy or rainy or both tomorrow? (to 2 dec pl)
the answer i got = 0.60

QUESTION TWO
Survey data showed that 65% of families had incomes over \$35,000, and 63% had two cars. According to the survey, the probability that a family has two cars if their income is over \$35,000 is 0.76. What is the probability that a family has two cars and an income over \$35,000? (to 3 dec pl)
i got = 0.494

QUESTION THREE
A building contractor tenders for a government office block and a sports gymnasium. The office contract is to proceed first and the contractor estimates that his firm has a 62% chance of being awarded this contract. If he fails to win the office contract, the contractor believes he has a 59% chance of winning the gym contract, though if successful with the office contract he believes the chance of winning falls to 27%. Determine the probability that the contractor wins both of the contracts (as a decimal to 3 dec pl).
i got = 0.167

Thanks so much!!
• Sep 3rd 2009, 05:04 AM
CaptainBlack
Quote:

Originally Posted by wik_chick88
hey everyone!! have a few questions that are for an economics subject but are basic stats stuff, and ive done them i just wanted someone to check if i have the right/wrong answer and help me if i have the wrong answer? thanks in advance!!

QUESTION ONE
Suppose that the probability that tomorrow will be rainy is 0.38 and the probability of it being windy tomorrow is 0.31. Also the probability that it will rain and be windy tomorrow is 0.09. What is the probability it will be windy or rainy or both tomorrow? (to 2 dec pl)
the answer i got = 0.60

Since the event thet it rains and is windy is included in bothe events it rains tommorow and it is windy tommorow if we add the probabilites that it rains tommorow and that it is windy tomorrow we have counted the event that it both rains and is windy tommorow twice, so we need to subtract it once to get the required answer.

Its a case of the inclusion-exclusion principal (yes the answer is 0.6).

CB
• Sep 3rd 2009, 05:07 AM
CaptainBlack
Quote:

Originally Posted by wik_chick88
QUESTION TWO
Survey data showed that 65% of families had incomes over \$35,000, and 63% had two cars. According to the survey, the probability that a family has two cars if their income is over \$35,000 is 0.76. What is the probability that a family has two cars and an income over \$35,000? (to 3 dec pl)
i got = 0.494

65% have incomes over \$35,000 and 76% of those have two cars, so 0.65x0.76x100% have two cars and an income over \$35,000.

(while requested 3 decimal places are not waranted for this result, its only good to 2 significant figures)

CB