Question

Please Answer all 5 questions (2,4,5,6, and 7)

Question 2: At a summer camp, 72% of the campers participate in rope climbing and 26% participate in canoeing. 83% of the campers participate in rope climbing, canoeing or both. what is the probability that a randomly selected camper participate in both rope climbing and canoeing.

Answer choices:  A) 0.11 B) 0.15 C) 0.69 D) 0.98 E) Cannot Be Determined

Question 4: According to school records, your school’s softball team wins 62% of the time when they play a game on their home field and 26% of the time when they play at the other team’s field. This season, they play 45% of their games at their home field. Assuming this team wins at the same pace as previous teams, what is the probability that they win a randomly selected game this season?

Answer Choices:  (A) 0.040 (B) 0.143 (C) 0.279 (D) 0.422  (E) 0.440

Question 5: Redundant monitoring means that a signal is sent in multiple forms or paths to reach its intended target. For example, an alarm may be set up to send multiple signals to a security company, each independent of each other in case of failure along one path. If an alarm sends off four signals down different paths, and each has a 0.65 probability of reaching the security company, what is the probability that at least one signal successfully reaches the security company?

Answer Choices: (A) 0.015 (B) 0.111 (C) 0.178 (D) 0.821 (E) 0.985

Question 6: A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean = 60 and standard deviation = 5. The number of miles that the extended life tires last has a mean = 70 and standard deviation = 7. If mileages for both tires follow a normal distribution, what is the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire?

Answer Choices: (A) 0.108 (B) 0.123 (C) 0.434. (D) 0.566 (E) 0.592

Question 7:  When playing the card game Blackjack, multiple decks are used and reshuffled often so that the outcomes of the cards dealt are approximately independent. When a player receives two cards that are a combination of an ace and a face card, this is called a “natural blackjack” and automatically wins. A natural blackjack should occur in 4.5% of the rounds played. What is the probability that a player plays 20 rounds of Blackjack and gets two or more natural blackjacks?

Answer Choices: (A) 0.059 (B) 0.168 (C) 0.227 (D) 0.773 (E) 0.900

Answer 1

2)

probability that a randomly selected camper participate in both rope climbing and canoeing

=P(rope climbing)+P(canoeing )-P(at least one) =0.72+0.26-0.83 =0.15

3)

probability that they win a randomly selected game this season\

=P(home game and wins)+P(away game and wins) =0.45*0.62+(1-0.45)*0.26=0.422

5)

probability that at least one signal successfully reaches the security company=1-P(none reaches)

=1-(1-0.65)^4 =0.985

6)

here mean difference =60-70 =-10

and standard deviaton =sqrt(5^2+7^2)=8.60

probability =P(X>0)=P(Z>(0--10)/8.602)=P(Z>1.16)=1-P(Z<1.16)=1-0.877=0.123

7)

here this is binomial with parameter n=20 and p=0.045

P(X>=2)=1-P(X<=1)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.227