[Admin]

in reply to: Cards #18903

All the hearts and black aces are removed from a standard pack of cards. If a card is drawn at random from the remaining cards, find the probability of drawing:
a. A red card.

b. An ace.

if all the hearts are removed – that leaves 39 cards and then remove two black aces, that leaves 37 cards 13 red cards left, and only one red ace

a. P(red) = $$\frac{13}{37}$$

b. P(Ace) = $$\frac{1}{37}$$

[Admin]

in reply to: Probability #18902

There is a 9 in 10 chance of a bird hatching and surviving in the Nullarbor Plain. From a nest of 3 chicks, find the probability that: a. All 3 chicks survive. b. No chicks survive. c. Exactly 2 chicks will survive.
a. P(SSS) = 9/10 × 9/10 × 9/10 = 729/1000	P(Survive) = 9/10  P(Dead) = 1/10 for them all to survive, there is only one way this can happen SSS
b. P(DDD) = 1/10 × 1/10 × 1/10 = 1/1000	for none to survive they all must be dead: DDD
c. P(2S, 1D) = P(SSD) + P(SDS) + P(DSS) =  9/10 × 9/10 × 1/10 +  9/10 × 1/10 × 9/10 +  1/10 × 9/10 × 9/10 = 243/1000	for 2 to survive, must consider all the ways this can happen SSD  where the first 2 survive and the last one dies SDS where the middle one dies DSS where the first one dies

[Admin]

in reply to: Probability #18900

Five cards are numbered 1, 2, 3, 4 and 5. Two cards are selected and placed together to form a 2-digit number. a. What is the probability of forming the number 43? b. What is the probability of an even number occurring?
12, 13, 14, 15 21, 23, 24, 25 31, 32, 34, 35 41, 42, 43, 45 51, 52, 53, 54	work out all of the possible digits doing this in an organised table is the most efficient and easy way
a. P(43) = 1/20	there are 20 numbers altogether and only one that forms 43
a. P(even) = 8/20 = 2/5	counting the even numbers, there are 8 of them

[Admin]

in reply to: Probability #18899

At a tropical holiday resort, the probability of rain on any day is 0.8. What is the probability that it will rain on a particular weekend?
P(rain on the weekend) = P(RR) + P(R-) + P(-R) = (0.8 × 0.8) + (0.8 × 0.2) + (0.2 × 0.8) = 0.96	we must consider all of the possibilities Rain on both Sat and Sun: R R Rain on Sat but not Sun: R – Rain on Sun but not Sat: – R

[Admin]

in reply to: Financial Expectation #18898

John plays a game in which he has a 20% chance of winning $50, a 50% chance of winning $10 and a 30% chance of losing $5. What is John’s financial expectation when playing this game?
P($50) = 0.2 P($10) = 0.5 P(-$5) = 0.3	each probability must be multiplied by the outcome, and the loss will be a negative outcome
E = 0.2 × 50 + 0.5 × 10 + 0.3 × -5 E = $13.50	calculate the expectation, which in this case is winning  $13.50

[Admin]

in reply to: Financial Expectation #18895

A coin is biased to that there is a 60% chance it will be heads when it is tossed.  If the coin is tossed and the result is “a head” you win $12 if the result is “a tail” you lose $15. Calculate the expected financial return.
P(H) = 0.6  win $12 P(T) = 0.4  lose $15	To obtain the Expectation (E) you must multiply the probability of the outcome by the financial return, remembering if it is a loss, then the number is negative
E = 0.6 × 12 + 0.4 × -15 = $1.20	so the expectation of the game is positive, which is a win, of $1.20

[Admin]

in reply to: Financial Expectation #18893

There is a game where there is a 20% chance of winning $50, 50% chance of winning $5 or losing $5 if no prize is won. What is the financial expectation of this game?

P(lose) = 0.3

E = 0.20 × $50 + 0.50 × $5 + 0.30 × -$5

= $11

[Admin]

in reply to: Two Way Table #18887

	Test Results
	Accurate	Not Accurate	Total
With Disease	130	70	200
Without Disease	250	50	300
Total	380	120	500

130 = Accurate positive: The number of people who were accurately told they do have the disease. ie, told they have it and do have it
70 = False negative: The number of people who were falsely told they do not have the disease. ie, told they do not have it and do have it
200 = The total number of people with the disease

250 = Accurate negative: The number of people who were accurately told that they do not have the disease. ie, told they do no have it and do not have it
50 = False positive: The number of people who were falsely told they have the disease. ie, told they have it and do not have it
300 = The total number of people without the disease

380 = Total number of accurate results
120 = Total number of false/inaccurate results
500 = Total number

Here is another table, set up slightly differently.

	Test Results
	Test Positive	Test Negative	Total
With Disease	130	70	200
Without Disease	250	50	300
Total	380	120	500

130 = Positive result + disease. So this would be an accurate positive. ie, told they have it and do have it
70 = Negative + disease. So this would be a false negative. ie, told they do not have it and do have it
200 = The total number of people with the disease

250 = Positive + no disease. So this would be a false positive. ie, told they have it and do not have it
50 = Negative + no disease. So this would be an accurate negative. ie, told they do no have it and do not have it
300 = The total number of people without the disease

380 = Total number of positive results
120 = Total number of negative results

[Admin]

in reply to: Two Way Table #18886

A new test has been developed for determining whether or not people are carriers of the Gaussian virus. A two way table was used to record the results.

	Test Results
	Positive	Negative	Total
Carrier Not Carrier	74 14 16 96		88 112
Total	90	110

a. How many people were tested?

b. A person selected from the group is not a carrier of the virus. What is the probability that the test results would show this?

c. For how many of the people tested were their test results accurate?

a. total = 88 + 112
= 200

b. there are 112 people that are not carriers, out of those 96 have a negative result – ie showing they are not a carrier
P = $$\frac{96}{112}$$

= $$\frac67$$

c.  an accurate result would mean:
carrier receiving a positive result = 74
non carrier receiving a negative result = 96
accurate = 74 + 96
= 170

[Admin]

in reply to: Heart Rate #18883

What is the MHR for a 20 year old?
MHR = 220 – 20	Use formula MHR = 220 – age in years
= 200 bpm	answer in units bpm (beats per minute)

[Admin]

in reply to: Fuel Consumption #18877

The fuel consumption for John’s car is 16.7 L/100km for Urban conditions. The combined fuel consumption is 12.4 L/100km. a. The fuel consumption for the Combined Test is the average of the Urban and Extra Urban (Freeway) rates. What is Extra Urban Fuel Consumption Rate? b. John travels to work 520km each month in Urban Conditions. How many litres of fuel per month does John use travelling to work? c. John travels to work for 11 months per year. How many kilograms of CO2 emissions would John’s car make?
a. $$12.4=\frac{16.7+x}{2}$$	to find average add Urban (16.7) to Extra Urban (x) and divide by 2
24.8 = 16.7 + x	multiply both sides by 2
x = 8.1	subtract 16.7 from both sides
8.1 L/100km
b. 520 ÷ 100 = 5.2	driving in Urban conditions uses 16.7 L/100km. Find how many lots of 100km in 520 km by dividing
5.2 × 16.7 = 86.84 L	this means that John used 5.2 lots of 16.7 L, so to find his fuel used multiply
86.84 L per month
c. 520 × 11 = 5720 km	if John does  per month, multiply by 11 to find fuel for the 11 months he travels to work
5720 × 291 = 1 664 520 grams	the CO2 os 291 g per km, since he did 5720 km, multiply
1 664 520 ÷ 1000 = 1644.52	convert to kg by dividing by 1000
1644.52 kg

[Admin]

in reply to: Fuel Consumption #18876

A car uses 7.28 litres of petrol per 100 km. If you were to go on a 315 km trip, how many litres of petrol would the car use?
315 ÷ 100 = 3.15	find out how many lots of 100km are in 315km by dividing this means we would need to buy 3.15 lots of 7.28 litres
3.15 × 7.28L = 22.932 L	to find the number of litres multiply 3.15 by 7.28

[Admin]

in reply to: Fuel Consumption #18875

A motorist started a trip with a full tank of petrol and after travelling 540km refilled the tank. Given that the refilling took $45 worth of petrol at 70.9 cents per litre. Calculate: a. the number of litres of petrol used on the trip. b. the consumption rate per hundred kilometres.
a. 70.9 ÷ 100 = $0.709	Step 1: Change the cents to dollars
45 ÷ 0.709 = 63.5 L	Step 2: Find out how many litres by dividing $45 by the cost per litre
b. 540 ÷ 100 = 5.4	Step 1: Since we are interested in how many litres per 100km, we need to find out how many lots of 100 are in 540 km
63.5 ÷ 5.4 = 11.76	Step 2: To find out how many litres per 100km, we need to divide the number of litres by the number of 100 km’s
∴ 11.76 L/100km

[Admin]

in reply to: Rates #18874

2.5 g of medicine is used to make a 300 mL solution. What is the concentration of this medicine in mg/mL?
2.5 × 1000 = 2500 mg	this means for every 3oo mL of solution, we need 2.5 g of medicine. first we need to change the g to mg by multiplying 2.5 by 1000
2500 ÷ 300 = 8.333..	we need to find out how much per 1 mL, so we need to divide by 3oo
8.3 mg/mL

[Admin]

in reply to: Rates #18872

A patient is prescribed 600mg of a painkiller. Calculate how much must be given if the medication is available in the concentrations: a. 20 mg in 5 ml b. 75 mg in 5 ml
a. 600 ÷ 20 = 30	this means for every 20 mg, we need 5 ml of painkiller, so we find out how many lots of 2omg are in 600 mg
8 × 5 ml = 40 ml	we need 8 lots of 20 mg, which means we need 8 lots of 5 ml

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