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**wansee_me** I need serious help with these ten problems...someone please help 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) = ....

PLEASE HELP ME...IT'S SO URGENT! THANKS!