Question

Part 1: Probability

1. A question on a multiple-choice test has 10 questions each with 4 possible answers (a,b,c,d).
What is the probability that you guess all the answers to the 10 questions correctly (earn 100%)?

2. If you ask three strangers about their birthdays, what is the probability
a. All were born on Wednesday?
b. What is the probability that all three were born in the same month?
c. All were born on different days of the week?
d. None was born on Saturday?

3. An automobile dealer decides to select a month for its annual sale. Find the probability that it will be September or October.
4. Consider the example of finding the probability of selecting a black card or a 6 from a deck of 52 cards.

5. The probability that s student owns a car is 0.65, and the probability that a student owns a computer is 0.82.

a. If the probability that a student owns both is 0.55, what is the probability that a randomly selected student owns a car or computer?
b. What is the probability that a randomly selected student does not own a car or computer?
6. If 2 cards are selected from a standard deck of cards. The first card is placed back in the deck before the second card is drawn. Find the following probabilities:
a) P(Heart and club) b) P(Red card and 4 of spades) c) P(Spade and Ace of hearts)

7. If 2 cards are selected from a standard deck of cards. The first card is not replaced in the deck before the second card is drawn. Find the following probabilities:
a) P(2 Aces) b) P(Queen of hearts and a King) c) P(Q of Hearts and Q of hearts )
8. A flashlight has 6 batteries, 2 of which are defective. If 2 are selected at random without replacement, find the probability that both are defective.
9. You take a trip by air that involves three independent flights. If there is an 80% chance each specific leg of the trip is on time, what is the probability all three flights arrive on time?

Answer 1

ANSWER :

1.

P(correct answer) = 1/4 

P( all 10 answers correct) 

= (1/4)^10  (ANSWER).

2.

a.

Wednesday is one out of 7 days.

=> P(Wednesday) = 1/7 

=> P(all 3 persons birthday is Wednesday)

= 1/7 *1/7*1/7

= 1/343 = 0.00292 approx. (ANSWER)

b.

P( all 3 born same month) = 1/12 * 1/2 * 1/12 = 1/1728 (ANSWER).

c.

P( all  born on different days) 

= 7/7 * 6/7 * 5/7 

= 30/49  (ANSWER)

d.

P(none born on Sunday) = 6/7 * 6/7 * 6/7 = 216/343 = 0.6297 approx. (ANSWER).

3.

P( sept. or oct.) = 1/12 + 1/12 = 1/6 (ANSWER) 

4.

P(black card or 6) = 26/52 + 4/52 - 2/52 = 28/52 = 4/13 (ANSWER).

5.

P(car or computer) = 0.65 + 0.82 - 0.55 = 0.92 (ANSWER).

6.

a. 

P(heart and club) = 13/52 * 13/52 = 1/16 (ANSWER).

b.

P(red card and 4 of spade) = 26/52 * 1/52 = 1/104 (ANSWER).

c.

P(Q of hearts and Q of hearts) = 1/52 * 1/52 = 1/ 2704 (ANSWER)

7.

a.

P(2 aces) = 4/52 * 3/51 = 1/221 (ANSWER) 

b.

P(Q of hearts and a King) = 1/52 * 4/51 = 1/663 (ANSWER) 

c. 

P(Q of hearts and Q of hearts) = 1/52 * 0 = 0 (ANSWER)

8.

P(both defective) = 2/6 * 1/5 = 1/15 (ANSWER)

9.

P( all 3 flights on time) = 0.8 * 0.8 * 0.8 = 0.512 (ANSWER)

Answer 2

Note: as per rules, first question of multiple questions is also allowed to solve unless you asked for a specific question. So i have solved for Question(1).

1) Binomial distribution : P(X = x) = n. *p** (1-p)"-* Where n = total number of trials X = number of success's we chosen out of n p = probability of success. n! 2) ncx = (%) = xlım-x) X = number of questions the student gets correct. Given that The number of questions n= 10. Each question has 4 options and only one option is correct. First find p. The probability that a randomly selected question correct = p = = = 0.25.

Now we have to find the probability that all 10 questions gets correct. i.e we have to find P(X = 10). P(X = 10) = 10cn* (0.25)10 + (1 - 0.25)10-10 = 10c10 * (0.25)10 * (0.75)° || 10! 101-(10-10); * (0.25)10 + 1 = 1* (0.25)10 = (0.25)10 = 4-10 .: P(X = 10) = 4-10