This module provides a number of homework exercises related to Probability.
Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.
= card drawn is green
= card drawn is even-numbered
List the sample space.
Are
and
mutually exclusive? Justify your answer numerically.
No
Refer to the previous problem. Suppose that this time you randomly draw two cards, one at a time, and
with replacement .
Draw a tree diagram of the situation.
Are
and
independent events? Explain why or why not.
Refer to the previous problems. Suppose that this time you randomly draw two cards, one at a time, and
without replacement .
= first card is green
= second card is green
Draw a tree diagram of the situation.
Are
and
independent events? Explain why or why not.
No
Roll two fair dice. Each die has 6 faces.
List the sample space.
Let
be the event that either a 3 or 4 is rolled first, followed by an even number. Find
.
Let
be the event that the sum of the two rolls is at most 7. Find
.
In words, explain what “
” represents. Find
.
Are
and
mutually exclusive events? Explain your answer in 1 - 3 complete sentences, including numerical justification.
Are
and
independent events? Explain your answer in 1 - 3 complete sentences, including numerical justification.
A special deck of cards has 10 cards. Four are green, three are blue, and three are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin.
List the sample space.
Let
be the event that a blue card is picked first, followed by landing a head on the coin toss. Find
.
Let
be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events
and
mutually exclusive? Explain your answer in 1 - 3 complete sentences, including numerical justification.
Let
be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events
and
mutually exclusive? Explain your answer in 1 - 3 complete sentences, including numerical justification.
Yes
No
An experiment consists of first rolling a die and then tossing a coin:
List the sample space.
Let
be the event that either a 3 or 4 is rolled first, followed by landing a head on the coin toss. Find
.
Let
be the event that a number less than 2 is rolled, followed by landing a head on the coin toss. Are the events
and
mutually exclusive? Explain your answer in 1 - 3 complete sentences, including numerical justification.
An experiment consists of tossing a nickel, a dime and a quarter. Of interest is the side the coin lands on.
List the sample space.
Let
be the event that there are at least two tails. Find
.
Let
be the event that the first and second tosses land on heads. Are the events
and
mutually exclusive? Explain your answer in 1 - 3 complete sentences, including justification.
Yes
Questions & Answers
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