Question

4. (22pt) Danielle is performing an experiment where she draws a random card from standard deck, rolls a 6 sided dice, and draws a marble from a bag with 4 red, 5 green, 10 blue, and 12 white. Use this information to answer the following questions (be sure to write all probability answers as fractions AND decimals with 3 place values): a. How big is the sample space? b. Write out, exactly, what 3 possible outcomes might be. c. Let event A be rolling less than a 3 on the die. How many outcomes of the experiment would be included in event a? (Hint: be careful and think about how many there are total.) d. Let event B be drawing a heart card. How many outcomes does B have in it? Write one possible outcome out explicitly. e. Let event C be drawing a blue marble and event D be drawing a red marble. Are C and D mutually exclusive? Are they independent? Justify. f. Write in words and find P(A and B). g. Write in words and find P(AIC) and P(A). What does comparing these two numbers tell us? h. Write in words and find P(D or B). i. Write in words and find P(BIC) j. Let event E be to draw a spade face card. Which events is E mutually exclusive with? Which events is E independent with? Show your work. Suppose we know E has already happened. What is the probability A, B, and D also happen? What is the notation for this?

Answer 1

As per the HomeworkLib guidelines I am suggested to answer only the first four parts, please ask the rest of the parts separately. I will be happy to help.

a) Sample Space = Number of cards * Numbers on the dice * Different colored marbles number

= 52 * 6 * 4

= 1,248

b) 3 possible Outcomes:

1) Ace of Heart, 6 , blue marble,

2) King of Spade, 4, white marble

3)Queen of Diamonds, 1, blue marble

c) Numbers less than 3 on dice = 2

Total outcomes = Number of cards * (Numbers on dice less than 3) * Different colored marbles number

= 52 * 2 * 4

= 416

d) Number of heart cards = 13

Total outcomes = Number of heart cards * Numbers on a dice * Different colored marbles

= 13 * 6 * 4

= 312

One such possible outcome: Ace of Heart, 6, white marble