# Help with Probability!

#### aisha00

##### New Member
Hi. I came across a few questions tht i came across while studyin for a probability chapter. Just a little request, im very new to probability so u could explain the steps if u get the answer, i've mentioned the correct answers 2. Here they go.

1)The probability that a person owns a microwave is 0.75, that a person owns a compact disk player is 0.25. and that a person owns both a microwave and a CD player is 0.16. Find the probability that a person owns either a a microwave or a CD player , but not both.

I did 0.75+0.25-0.16=0.84 BUT the answer is 0.68.

2)A physics test contains 25 true/false questions. How many different possible answer keys can be made?

I can't seem to even get started on this 1. The answer is 335,554,432

3)License plates are to be issued with 3 letters followed by 4 single digits.
a)How many such license plates are possibble? b)If the plates are issued at random, what is the probability that the license place says USA followed by a number that is divisible by 5?

The question doesn't mention if the letters/ digits can be repeated which is whts confusing me. And since it says 4 single digits, they should all be less than 10 right? The right answer is a)175,760,000 b)0.0000114

4)A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting a disease if a person is not vaccinated is 50%. In a certain geographic region, 25% of the people get vaccinated. If a peron is selected at random, find the probabilty that he/she will contract the disease.

10% is the chance of the vaccine being not effective.
50% chance of getting disease if not vaccinated.
75% in that region are not vaccinated.

75% have a 50% chance of getting it and the 25% have a 10% chance of getting it. So I do 75/50 + 25/10 = 4, but the answer is 0.4.

5)Several territories and colonies today are still under the jurisdiction of another country. France holds the most with 16 countries, the United Kingdom has 15, the United States has 14, and several other countries have territories as well. Choose 3 territories at random form those held by France, the United Kingdom, and the United States. What is the probability that all 3 belong to the same country?

I can't start on this one aswell :'(. The correct answer is 0.097

Thankyou all

#### poipoi

##### New Member
Hi !

2)A physics test contains 25 true/false questions. How many different possible answer keys can be made?
I can't seem to even get started on this 1. The answer is 335,554,43
for each qustion, you have two different answer possible. so for the first question 2 possibilities, for the second, 2 possibilities ..
so you have 2^25 possible answers (=335,554,432)

3)License plates are to be issued with 3 letters followed by 4 single digits.
a)How many such license plates are possibble? b)If the plates are issued at random, what is the probability that the license place says USA followed by a number that is divisible by 5?
The question doesn't mention if the letters/ digits can be repeated which is whts confusing me. And since it says 4 single digits, they should all be less than 10 right? The right answer is a)175,760,000 b)0.0000114[/COLOR]
you have 26 different letters, so 26 possibilities for the first letter, 26 for the second and 26 for the third. you have 10 different digit (0 to 9), so 10 for the first digit, ...
26^3 * 10^4 = 175,760,000

b. having a U in the first place have a probability of 1/26, having a S in the second is the same, ..
and whatever the number, you have 2 possibility that it will be divisible by 5 (the last digit should be a 0 or a 5, but not a 1, 2, 3, 4, 6, 7, 8, 9).
so ... (1/26)^3 * (2/10) = 0.0000114

4)A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting a disease if a person is not vaccinated is 50%. In a certain geographic region, 25% of the people get vaccinated. If a peron is selected at random, find the probabilty that he/she will contract the disease.
10% is the chance of the vaccine being not effective.
50% chance of getting disease if not vaccinated.
75% in that region are not vaccinated.

75% have a 50% chance of getting it and the 25% have a 10% chance of getting it. So I do 75/50 + 25/10 = 4, but the answer is 0.4.[/COLOR]
probability of being contractiing the disease:
1. if the person is vaccined : 1/10
2. if the person is not : 1/2
25/100 of person are vaccined, and 75/100 not,
so .. 25/100 * 1/10 + 75/100 * 1/20 = .4

5)Several territories and colonies today are still under the jurisdiction of another country. France holds the most with 16 countries, the United Kingdom has 15, the United States has 14, and several other countries have territories as well. Choose 3 territories at random form those held by France, the United Kingdom, and the United States. What is the probability that all 3 belong to the same country?

I can't start on this one aswell :'(. The correct answer is 0.097[/COLOR]
the three country have 16+15+14 country at all.
you have 16 chance on 45 of helding a french country at first. If its the case, you have then 15 chance on 44 of helding a french country a second time, and 14 out of 43 the third time ...
and so on for the other country,
so.. (16/45 * 15/ 44 * 14/ 43) + (15/45 * 14/44 * 13 / 43) + (14/45 * 13/44 * 12 / 43) = 0.097

Hope it helps ..!

#### aisha00

##### New Member
OMG, U're a genius! Thank u SO much .

#### poipoi

##### New Member
you're welcome !
I just realize I forgot to answer to the first question ..

)The probability that a person owns a microwave is 0.75, that a person owns a compact disk player is 0.25. and that a person owns both a microwave and a CD player is 0.16. Find the probability that a person owns either a a microwave or a CD player , but not both.
I did 0.75+0.25-0.16=0.84 BUT the answer is 0.68.
a person owns a microwave is 0.75
a person owns a compact disk player is 0.25
both a microwave and a CD player is 0.16

so the probability to own ONLY a microwave is .75-.16 = .59
and the probability to own ONLY a compact disk player is 0.25 -0.16 = 0.09
So, the probability to own only a microwave OR only a compact disk player is 0.59+0.09 = 0.68

#### aisha00

##### New Member
I know u got the right answer for the 1st 1 but my question dont u have to subrtract whts common just ONCE and not twice? The formula is P(A)+P(B)-P(A and B), so dont we subtract only once and not twice? If twice, why so? I'm getting confused. THankyou.

you're welcome !
I just realize I forgot to answer to the first question ..

a person owns a microwave is 0.75
a person owns a compact disk player is 0.25
both a microwave and a CD player is 0.16

so the probability to own ONLY a microwave is .75-.16 = .59
and the probability to own ONLY a compact disk player is 0.25 -0.16 = 0.09
So, the probability to own only a microwave OR only a compact disk player is 0.59+0.09 = 0.68

#### Dason

I know u got the right answer for the 1st 1 but my question dont u have to subrtract whts common just ONCE and not twice? The formula is P(A)+P(B)-P(A and B), so dont we subtract only once and not twice? If twice, why so? I'm getting confused. THankyou.
First off the formula is P(A or B) = P(A) + P(B) - P(A and B). This is not the case you're in.

Keep this is mind: you don't want to include people that own both appliances. Consider the formula you use: P(A) + P(B) - P(A and B). A person that owns both is in both A and B so they get counted twice but removed once. So they are still in the end probability which you don't want.