QR Probability question

[299678]

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Jim reaches into a basket containing the letters of the word CANTEEN and randomly pulls out two letters. What is the probability that one letter is a consonant and the other is vowel in any order?

 

[299678]

Q. It is known that 20% of the population of smallville has blue eyes. IF four people are chosen at random from this population, what is the probability that at least one of the four has blue eyes?

 

[299678]

Q. a bag contains 7 walnuts, 4 cashews, and 3 pistachio nuts. Two of the nuts fall out at random. What is the probability that one is a cashew and the other is a walnut?

 

[299678]

average kinetic energy for a molecules is proportional to absolute temperature

I am wondering if it is directly proportional? or not

 

[redchesus]

I forget how to do the one about blue eyes, but the rest I can do:

1) probability of getting a consonance then vowel + probability of getting vowel then consonance:
(4/7)(3/6) + (3/7)(4/6)

2) probability of getting cashew then walnut + probability of getting walnut then cashew:
(4/14)(7/13) + (7/14)(4/13)


Average kinetic energy is directly related to temperature, the higher the temp, the faster the molecules are moving (this is talking about ALL the molecules, hence average, because individual molecules are moving at different random speeds)

 

[UCB05]

Q. It is known that 20% of the population of smallville has blue eyes. IF four people are chosen at random from this population, what is the probability that at least one of the four has blue eyes?

The answer is complementary to the probability that none have blue eyes

Probability of none with blue eyes = (4/5)^4 =256/625
Probability of at least one with blue eyes = 1 - (4/5)^4 = 369/625

 

[299678]

Directly related means if we double up the temperature, the kinetic energy will be exactly double?

 

[redchesus]

Directly related means if we double up the temperature, the kinetic energy will be exactly double?

No, by directly I mean "not inversely", that is if you increase temperature, you increase avg. KE

if you wanted to figure out the actual ratio, you'd have to go through

PV = nRT
KE = 1/2 mv^2
and another equation I forget, it might have been a rate law

anyway, that requires calculus so I don't bother with it

 

[winnie bear]

No, by directly I mean "not inversely", that is if you increase temperature, you increase avg. KE

if you wanted to figure out the actual ratio, you'd have to go through

PV = nRT
KE = 1/2 mv^2
and another equation I forget, it might have been a rate law

anyway, that requires calculus so I don't bother with it

The other equation might be root mean squared speed, urms=sq rt (3RT/molar mass) and use this to substitute v in KE....not sure though.