Question

a. The probability that the temperature will fall below 32 degrees Fahrenheit on any given day is 20%. If the temperature does fall below 32 degrees, then there is an 80% chance of ice/frost. What is the probability that on any given day, the temperature will fall below 32 degrees and there will be ice/frost?

(Input answer as a decimal, rounded to three decimal places if necessary

b.In the card game Pokemon, players must construct a 60-card deck to play the game. In one such deck, there are 11 Pokemon, 16 energies, and 33 trainers. If three cards are randomly selected from the deck, what is the probability that all of them will be trainer cards?

(Input answer as a decimal, rounded to three decimal places if necessary)

c.A random sample of working adults found that 37% access the internet at work, 44% access the internet at home, and 21% access the internet at both work and home. What is the probability that a person in this sample selected at random accesses the Internet at work given that they access the internet at home?

d.A campus committee consists of 11 employees. We must choose 4 of these employees to
complete a task by the end of next week. How many ways can we choose a group to complete the task?

e.John runs a computer store. Yesterday he counted 116 who walked by his store, of whom 66 came into the store. Estimate the probability that a person who walks by the store will enter the store.

f.A store owner opens up a large shipment of shirts of various colors. It is found that the shipment has approximately 57% blue shirts. An employee of the store randomly selects five shirts to put on display. Find the probability that at least one of the selected shirts is blue.

Answer 1

a)

Let A be the event that the temperature will fall below 32 degrees Fahrenheit on any given day

B be the event that there will be ice/frost

The probability that the temperature will fall below 32 degrees Fahrenheit on any given day

The probability that there will be an ice frost given that the temperature will fall below 32 degrees Fahrenheit

The probability that on any given day, the temperature will fall below 32 degrees and there will be ice/frost =  

b) Total number of ways to select 3 cards from 60 cards is

Total number of ways 3 cards were trainer cards =

The probability that all of them will be trainer cards =

c) Let A be the event that working adult access the internet at work

B be the event that the working adult accesses the internet at home

The probability that a person in this sample selected at random accesses the Internet at work given that they access the internet at home is a conditional probability

d) This is a problem of Combination

Total number of ways to select 4 employees from 11 employees is

e) The probability that a person who walks by the store will enter the store =-

f) The probability that the shirt is blue shirt is

The probability that the shirt is not blue is

This probability is the same and independent of every shirt

now 5 shirts are selected at random to put on display

the probability that at least one of the selected shirts is blue.= 1- the probability none of the shirts is blue

The probability that none of the shirts is blue =

the probability that at least one of the selected shirts is blue. = 1-0.0147 = 0.9853

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