1. ## probability

1.) What is the probability of a person getting at least one question right on a multiple choice test with 10 questions (choices A-D for each question), if they guess at all of the questions?

2.) The daily number is a 3 digit number ranging from 000-999, and each of the three digits is drawn from a bin with digits 0-9.
a.) What is the probability of getting at least one of the numbers right?
b.) What is the odd against getting at least one of the numbers right?

3.) There are 5 senators and 3 representatives to form a 4 person committee. What is the probability that there will be the same number of senators and representatives?

4.) If a person is dealt a 5 card hand from a standard deck of playing cards, what is the probability that the person is dealth a pair ( 2 cards of the same rankL 2's, 3's, 4'w, ...)?

5.) On hundred students were surveyed, and 25% said they like math, 45% said they like english, and 5% said they like both math and english. IF a students is randomly surveyed what is the probability that they student does not like math or english?

6.) A shipment of ten calculators contains two defective ones. If you randomly choose four calculators, what is the probability that exactly one will be defective?

7.) A nickel, dime, and a quarter are tossed. What is the probability that the nickel and dime will show heads and the quarter will show tails?

8.) Which has a greater probability: drawing an ace and a ten card (ten, jack, queen, or king) from a regular deck of 52 cards, or drawing an ace and ten card from two decks of regular playing cards?

9.) What is the probability of being dealth an ace and a king if you are dealt two cards from a standard deck of cards?

10.) What is the probability of guessing someone's MAC pin number if you know the first two digits of the four digit pin number (assume the pin number is random)?

2. Originally Posted by wansee_me

1.) What is the probability of a person getting at least one question right on a multiple choice test with 10 questions (choices A-D for each question), if they guess at all of the questions?

Mr F says: 1 - Pr(get none right).

2.) The daily number is a 3 digit number ranging from 000-999, and each of the three digits is drawn from a bin with digits 0-9.
a.) What is the probability of getting at least one of the numbers right?
b.) What is the odd against getting at least one of the numbers right?

Mr F says: This makes no sense to me as written. Do you mean correctly guessing one of the numbers in the three digit number? In its correct position?

3.) There are 5 senators and 3 representatives to form a 4 person committee. What is the probability that there will be the same number of senators and representatives?

Mr F says: $\displaystyle {\color{red}\frac{{5 \choose 2} \cdot {3 \choose 2}}{{4 \choose 8}}}$.

4.) If a person is dealt a 5 card hand from a standard deck of playing cards, what is the probability that the person is dealth a pair ( 2 cards of the same rankL 2's, 3's, 4'w, ...)?

Mr F say: Suppose the pair is 2 Kings. The Kings can be chosen in $\displaystyle {4 \choose 2} = 6$ ways.

But the actual face value of the pair can be chosen in 13 ways.

And now you need to choose 3 more cards, none of which match each other. So choose 3 cards out of the 12 remaining values: $\displaystyle {12 \choose 3} = 220$ ways.

But each card can be 1 of the 4 suits, and so there are (4)(4)(4) = 64 ways to choose the suits.

Therefore the total number of ways is (6)(13)(220)(64).

Divide by $\displaystyle {52 \choose 5}$ to get the probability.

5.) On hundred students were surveyed, and 25% said they like math, 45% said they like english, and 5% said they like both math and english. IF a students is randomly surveyed what is the probability that they student does not like math or english?

Mr F says: Pretend there's 100 students and draw a Venn Diagram.

6.) A shipment of ten calculators contains two defective ones. If you randomly choose four calculators, what is the probability that exactly one will be defective?

Mr F says: $\displaystyle {\color{red}\frac{{8 \choose 3} \cdot {2 \choose 1}}{{10 \choose 4}}}$.

7.) A nickel, dime, and a quarter are tossed. What is the probability that the nickel and dime will show heads and the quarter will show tails?

Mr F says: Obviously Pr(HHT) = (1/2)(1/2)(1/2).

8.) Which has a greater probability: drawing an ace and a ten card (ten, jack, queen, or king) from a regular deck of 52 cards, or drawing an ace and ten card from two decks of regular playing cards?

Mr F says: 20/52 versus 40/104 ....

9.) What is the probability of being dealth an ace and a king if you are dealt two cards from a standard deck of cards?

Mr F says: Pr(AK) + Pr(KA) = (4/52)(4/51) + (4/52)(4/51) = ....

10.) What is the probability of guessing someone's MAC pin number if you know the first two digits of the four digit pin number (assume the pin number is random)?

Mr F says: (1/10)(1/10) = ....