Math 10 Name Exam 4: Chapter 12

Each problem is worth 10 points. You must show all work to receive full credit. Round to 3"* decimal place if necessar)'.

1. State whether each statement is true or false.

a. A coin that was flipped 100 times landed on heads 37 times, so the theoretical probability is P{heads) - ^ . ^ f e f e ^

b. The formula for finding the probability of Event A or Event B is P{A or B) = P{A) + P{B), when Events A and B are mutually exclusive. itu.t

c. The formula for finding the probability of Event A and Event B is P{A and B) = P{A) • P{B I given that A has aheady occured).

4 26 d. Say you choose a card from a deck of 52, P(J) = — , /"(black card) = — , then

32 32

P(J or black card) = 30 52

e. If PiA) = 0.75 , then P{not A) = - . 4

f The Counting Principal states that i f a first experiment can be performed in M distinct ways and a second experiment can be performed in N distinct ways, then Q . the two experiments in that specific order can be performed in M + N distinct ways. J C I \ S ^ '

g. For any two events. E l and E2, the conditional probability, P (E2 | E l ) , is n(ElandE2)

determined as follows. P{E2 \) = «(E2)

h. „C^-P. is true for all n and r. n r n r

i- ~nP\s true for all n.

J- «Q=«^„ is true for all n

2. If P(A)=0.7, P(B)=0.4, and P(A or B)=0.65, then find P(A and B).

). When playing bingo, 75 balls are placed in a bin and balls are selected at random. Each ball is marked with a letter and number as indicated in the following chart. Assuming ONE bingo ball is selected at random,

B I N „ G

1 - 1 5 1 6 - 3 0 3 1 - 4 5 4 6 - 6 0 6 1 - 7 5

t i u i i M K N v i i H p n n n i l ' "

a. Determine the probability that the ball selected is numbered greater than 15 and less than 41.

b. Determine the probability that the ball selected is lettered N or G.

•¥5 5 c Determine the probability that the ball selected is lettered N or G O R numbered greater than 15 and

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d. Detennine the probability that the ball selected is lettered N A N D numbered greater than 15 and less

e. Determine the probability that the ball selected is numbered an even number given that the ball selected is lettered B. -V

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4. At a local restaurant, each lunch special consists of a sandwich, a salad, and a beverage. The sandwich choices are roast beef (R), ham (H), or turkey (T). The salad choices are macaroni (M) or potato (P). The beverage choices are coffee (C) or soda (S).

Sandwich Salad Beverage Sample Space

RMC • ^ s RMS

P • RPC

r -—- s RPS

HMC s HMS

p - — - HPC r .— —~- s HPS

M e d T M C

M e d —~s TMS

- — s TPC TPS

a. Find P(ham sandwich or soda are selected).

2-

b. Find P(ham sandwich and soda are selected).

c. Find P(neither roast beef sandwich nor potato salad are selected).

d. Find P(coffee is selected | given a turkey sandwich was selected).

e. Find P(macaroni salad and soda are selected | given a turkey sandwich was selected).

5. Three marbles are drawn from a box with 5 white, 3 green, 2 red, and 4 blue marble.

a. Find P(all 3 marbles are blue), if the marbles were drawn one at a time with replacement.

b. Find P(all 3 marbles are blue), if the marbles were drawn one at a time without replacement.

1_ 3=^ J 2M _ .A

c. Find P ( r ' marble is blue, 2"'̂ marble is blue, and 3''' marble is green), i f the marbles were drawn one at a time with replacement.

1

d. Find P(l^' marble is blue, 2"*̂ marble is blue, and 3'̂ '' marble is green), i f the marbles were drawn one at a time without replacement.

e. Say the marbles were drawn at the same time. Use combinations to find P(2 marbles are blue and 1 marble is green, regardless of order), if the marbles were drawn at the same time without replacement.

6. A license plate is to consist of 3 letters followed by 3 digits (0-9). Determine the number of different license plates possible i f a. Repetition of letters and numbers is permitted.

L L L # # « ^

b. Repetition of letters and numbers is NOT permitted.

i , L L # # # \ — , „ -—A

c. The 1̂ ' letter has to be from the first four letters of the alphabet {a, b, c, d) and the 1'' number has to be greater than 6. Also, repetition of letters and numbers is permitted.

L L L » » » J \

d. The letter has to be from the first four letters of the alphabet {a, b, c, d) and the number has to be greater than 6. Also, repetition of letters and numbers is NOT permitted.

7. How many ways can you arrange the word T A L L A H A S S E E ?

You want to arrange the following 7 shapes in a row.

A O O i5r O 9 a. How many different ways can all 7 shapes be arranged?

J iL .2.̂ = \̂5c-4o\

b. How many different ways can the 7 shapes be arranged if the triangle is in the middle?

c. How many different ways can the 7 shapes be arranged if the triangle is m the middle and the star i on the end?

d. How many different ways can the 7 shapes be arranged if the square is first, the triangle is in the middle, and the star is on the end?

i _L .2^-L-L= 2^

How many different ways can the shapes be arranged if you can only arrange 4 of the 7 shapes?

3_ 6HO

9. Say a company that has 9 people in the marketing department and 11 people in the sales department has a lottery to raffle off ̂ prizes.

a. Find the number of different combinations the company can award the 5 prizes.

b. Find the number of different combinations the company can award the 5 prizes, i f all 5 of the prizes are awarded to the marketing department.

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c. Find the number of different combinations the company can award the 5 prizes, if all 5 of the prizes are awarded to the sales department.

d. Find the number of different combinations the company can award the 5 prizes, if 2 of the prizes are awarded to the marketing department and 3 of the prizes are awarded to the sales department.

e. Find the number of different combinations the company can award the 5 prizes, i f 3 of the prizes are awarded to the marketing department and 2 of the prizes are awarded to the sales department.

10. A television game show has five doors, of which the contestant must pick two. Behind two of the doors are expensive cars, and behind the other three doors are consolation prizes. The contestant gets to keep the items behind the two doors she selects. Determine the probability that the contestant wins

a. Find P(no cars).

P( /ic cars)= IC

b. Find P(at least one car).

p(al lmi-Cdr)= I- P/̂ no.fW IC

c. Find P(exactly one car).

IC

6 T ,2i lO ) '5 V

d. Find P(both cars).

lO

e. Find P(three cars).