Statistics and Probability Answers

There were ten red bottles sitting on the wall. The probability of a red bottle accidentally falling is 0.95. What is the probability that fewer than 8 of the green bottles accidentally fall?

5. QUESTION:

You consult Joe the bookie as to the form in the 2.30 at Ayr. He tells you that, of 16 runners, the favourite has probability 0.3 of winning, two other horses each have probability 0.20 of winning, and the remainder each have probability 0.05 of winning, excepting Desert Pansy, which has a worse than no chance of winning. What do you think of Joe’s advice?

4. QUESTION:

M&M sweets are of varying colours and the different colours occur in different proportions. The table below gives the probability that a randomly chosen M&M has each colour, but the value for tan candies is missing.

Colour Brown Red Yellow Green Orange Tan

Probability 0.3 0.2 0.2 0.1 0.1 ?

(a) What value must the missing probability be?

(b) You draw an M&M at random from a packet. What is the probability of each of the following events?

i. You get a brown one or a red one.

ii. You don’t get a yellow one.

iii. You don’t get either an orange one or a tan one.

iv. You get one that is brown or red or yellow or green or orange or tan.

3. QUESTION:

A bag contains fifteen balls distinguishable only by their colours; ten are blue and five are red. I reach into the bag with both hands and pull out two balls (one with each hand) and record their colours.

(a) What is the random phenomenon?

(b) What is the sample space?

(c) Express the event that the ball in my left hand is red as a subset of the sample space.

2. QUESTION:

A fair coin is tossed, and a fair die is thrown. Write down sample spaces for

(a) the toss of the coin;

(b) the throw of the die;

(c) the combination of these experiments.

Let A be the event that a head is tossed, and B be the event that an odd number is thrown. Directly from the sample space, calculate P(A ∩ B) and P(A ∪ B).

1. QUESTION:

Describe the sample space and all 16 events for a trial in which two coins are thrown and each shows either a head or a tail.

A lot consists of 10 good articles, 4 with minor defects and 2 with major defects. i. One article is chosen at random. Find the probability that (a) It has no defects, (b) It has no major defects, (c) It is either good or has major defects. ii. Two articles are chosen (without replacement), Find the probability that (a) Both are good (b) Both have major defects (c) At least one is good (d) at most one is good (e) Exactly one is good (f) Neither has major defects  

the time between busses on stevens creek blvd is 12 minutes. Therefore the wait time of a passenger who arrives randomly at a bus stop is uniformly distributed between 0 and 12 minutes.

a. find the probability that a person randomly arriving at the bus stop to wait for the bus has a wait time of at most 5 minutes.

in the accompanying diagram, the shaded area represents approximately 95% of the scores on a standardized test. If these scores ranged from 78 to 92,

a. what is the mean?

b. what is the standard deviation?

. In a manufacturing organisation, the distribution of wages was perfectly

normal and the number of workers employed in the organisation was 5000.

The mean wages of the workers were calculated at Rs. 800 and standard

deviation was worked out to be Rs. 200. On the basis of the information

estimate:

(i) The number of workers getting salary between Rs.700 and Rs.900.

(ii) Percentage of workers getting salary above Rs.1000

(iii) Percentage of workers getting salary below Rs.600

5. QUESTION:

You consult Joe the bookie as to the form in the 2.30 at Ayr. He tells you that, of 16 runners, the favourite has probability 0.3 of winning, two other horses each have probability 0.20 of winning, and the remainder each have probability 0.05 of winning, excepting Desert Pansy, which has a worse than no chance of winning. What do you think of Joe’s advice?