Hi! I have 4 math questions! (:
1.) There is a 10% chance it will rain on Saturday and a 30% chance it will rain on Sunday. What percent chance is there that it will rain on both Saturday and Sunday?
2.)In a shipment of alarm clocks, the probability that one alarm clock is defective is 0.04. Charlie selects three alarm clocks at random. If he puts each clock back with the rest of the shipment before selecting the next one, what is the probability that all three alarm clocks are defective?
3.) A builder has 8 lots available for sale.
·Six lots are greater than one acre.
·Two lots are less than one acre.
What is the probability that the next three lots sold will be greater than one acre?
4.) A cafeteria has 5 turkey sandwiches, 6 cheese sandwiches, and 4 tuna sandwiches. There are two students in line and each will take a sandwich. What is the probability that the first student takes a cheese sandwich and the next student takes a turkey sandwich? 2/15
1, 2. If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
3. 8 lots total. With each selection, there is one less large lot and one less total.
6/8 * 5/7 * 4/6 = ?
4. 6/15 * 5/14 = ?
In a shipment of alarm clocks, the probability that one alarm clock is defective is 0.04. Charlie selects three alarm clocks at random. If he puts each clock back with the rest of the shipment before selecting the next one, what is the probability that all three alarm clocks are defective?
1.) To find the probability that it will rain on both Saturday and Sunday, you can multiply the individual probabilities. So, the probability of rain on Saturday is 10% (0.10) and the probability of rain on Sunday is 30% (0.30). Multiply these probabilities together: 0.10 x 0.30 = 0.03, which is 3%. Therefore, there is a 3% chance it will rain on both Saturday and Sunday.
2.) Since Charlie selects three alarm clocks at random and puts each clock back with the rest of the shipment before selecting the next one, we can treat each selection as an independent event. The probability that one alarm clock is defective is 0.04. To find the probability that all three alarm clocks are defective, we can multiply the individual probabilities together. So, the probability of one alarm clock being defective is 0.04 (4%). Multiply this probability three times to get: 0.04 x 0.04 x 0.04 = 0.000064, which is 0.0064%. Therefore, there is a 0.0064% chance that all three alarm clocks Charlie selects are defective.
3.) To find the probability that the next three lots sold will be greater than one acre, we need to consider the total number of lots (8), the number of lots greater than one acre (6), and the number of lots less than one acre (2). Since the lots are being sold one at a time, we can treat each sale as an independent event.
The probability of the first lot being greater than one acre is 6/8 (or simplified, 3/4). After the first lot is sold, there are now 7 lots remaining, with 5 lots greater than one acre and 2 lots less than one acre.
The probability of the second lot being greater than one acre, given that the first lot was already sold, is 5/7. After the second lot is sold, there are now 6 lots remaining, with 4 lots greater than one acre and 2 lots less than one acre.
The probability of the third and final lot being greater than one acre, given that the first two lots were already sold, is 4/6 (or simplified, 2/3).
To find the combined probability, we multiply the individual probabilities together: (3/4) x (5/7) x (2/3) = 30/84 (or simplified, 5/14). Therefore, there is a 5/14 chance that the next three lots sold will be greater than one acre.
4.) To find the probability that the first student takes a cheese sandwich and the next student takes a turkey sandwich, we need to consider the total number of sandwiches available (5 turkey sandwiches, 6 cheese sandwiches, 4 tuna sandwiches) and the number of sandwiches that meet the desired criteria (1 cheese sandwich and 5 turkey sandwiches).
The probability that the first student takes a cheese sandwich is 6/15. After the first sandwich is taken, there are now 14 sandwiches remaining, with 5 turkey sandwiches remaining.
The probability that the next student takes a turkey sandwich, given that the first student took a cheese sandwich, is 5/14.
To find the combined probability, we multiply the individual probabilities together: (6/15) x (5/14) = 30/210 (or simplified, 1/7). Therefore, there is a 1/7 chance that the first student takes a cheese sandwich and the next student takes a turkey sandwich.