Dependent or Independent
Are the following events independent or dependent?
You pick a card out from a standard deck and then flip a coin.
Independent
Two events that cannot happen simultaneously are...
mutually exclusive
A bowl contains four apples, three bananas, three oranges, and two pears. If one piece of fruit is selected at random, what is the probability of selecting an orange?
3/12=1/4
What are the odds of choosing a diamond from a standard deck of cards?
P(s)= 13/52=1/4
How to read P(Like Chocolate | Like Vanilla)
Probability someone like Chocolate given than that person also like Vanilla
You pick a card out of a deck, put it back, then pick another card
Are these events independent or dependent?
Independent
At a local high school, 34% of the students take a bus to school and 56% of the students walk to school. Find the probability of randomly selecting a student that takes a bus or walks to school and determine if these events are mutually exclusive or non mutually exclusive event?
34/100 + 56/100 = 90/100 or 90%
P(A or B)= P(A)+ P(B)
mutually exclusive
What is the probability of selecting a yellow or blue marble from a box of 5 green, 3 yellow, and 2 blue marbles?
P(yellow or blue)= P(yellow) + P(blue) = 5/10=1/2
What is the probability of tossing 3 heads when three coins are tossed?
1/2*1/2*1/2=1/8
P(A|B) is equal to P(A and B) divided by ...
P(B)
You flip a coin and then flip the same coin again.
A) Are these events independent or dependent?
B) Find the probability of getting two heads
A) Independent
B) 1/2 * 1/2= 1/4
A card is drawn from a standard deck of cards. What is the probability of drawing a Jack or a Heart?
A) Are these events mutually exclusive or non mutually exclusive event?
B) Determine the probability of the event
A) non mutually exclusive event event
B) 4/52 + 13/52 - 1/52 =16/52= 4/13
What is the probability of rolling two dice and getting a sum greater than 10
(5,6), (6,5), or (6,6)
3/36= 1/12
Ms. E was planning a trip to the beach on Saturday but the weather forecast states that the chance of rain on Saturday is 65%. What is the probability that it won't rain on Saturday?
P(no rain)= 35/100
A number is selected, at random, from the set {1,2,3,4,5,6,7,8} .
Find P(Prime|odd)
The probability of randomly selecting two dimes from a bag containing 10 dimes and 8 pennies if the first selection is replaced
A) Are these events independent or dependent?
B) Determine the probability of selecting two dimes
A) Independent
B) 10/18 * 10/18 =100/324= 25/81
On a school board, 2 of the 4 female members are over 40 years of age, and 5 of the 6 male members are over 40. If one person did not attend the meeting, what is the probability that the person was a male or a member over 40?
4/5
P(male or over 40)= P(male) + P(over 40) - P(male and over 40) = 6/10+ 7/10 - 5/10= 8/10= 4/5
A bag contains 3 black, 5 green, and 4 yellow marbles.
What is the probability that 2 marbles selected a random will both be black?
P(2 black marbles)= 3/12*2/11=6/132= 1/22
Two number cubes are tossed. What are the odds that they show a sum greater than 9?
6/36=1/6 (5,5)(4,6)(6,4)(5,6)(6,5)(6,6)
A family that is known to have two children is selected at random from amongst all families with two children. Find the probability that both children are boys, given that there is a boy in this family.
1/3
P(A and B) = 1/5
P(A) = 1/3
P(B) = 3/5
Are A and B Independent event? Explain your answer
Yes.
because P(A and B) = P(A) x P(B)
The probability of selecting a card from a standard deck of cards and the card is a 10 or an ace
A) Determine if the event is mutually exclusive or non mutually exclusive event and
B)Determine the probability
A) Mutually exclusive
B) 4/52 + 4/52= 8/52 = 2/13
Find the probability of randomly selecting 3 red pencils from a box containing 5 red, 3 blue, and 4 green pencils
5/12*4/11*3/10=60/1320=1/22
If two marbles are selected at random from a bag containing 6 red and 4 blue marbles, find the odds that both marbles are red.
P(both red)= 6/10*5/9=30/90= 1/3
A coin is tossed. If it shows heads, a marble is drawn from Box 1, which contains one white and one black marble. If it lands tails, a marble is drawn from Box 2, which contains two white and one black marble. Find: a) P(black | coin fell heads)
b) P(white | coin fell tails)
a) 1/2
b) 2/3
There are two traffic lights along the route that Ms. Bella drives from home to work. One traffic light is red 50% of the time. The next traffic light is red 60% of the time. The lights operate on separate timers. Find the probability that these lights will both be red on Ms. Bella's way home from work.
A) Are these events independent or dependent?
B) Determine the probability that both lights will be red
A) Independent
B) 50/100 * 60/100 = 3/10 or 30%
A card is selected from a standard deck of cards. What is the probability of selecting an Ace or a black card?
A) Are these events mutually exclusive or non mutually exclusive event?
B) Determine the probability
A) non mutually exclusive event
B) 4/52 + 26/52 - 2/52 = 28/52 = 7/13
A survey of the junior class at SPF high school shows that 2/5 of the students who have home computers use them for word processing, 1/3 use them for playing games, and 1/4 use them for both word processing and playing games. What is the probability that a student with a home computer uses it for word processing or playing games?
29/60
P(AorB)= P(A) + P(B) - P(AandB)
P(AorB)= 2/5 + 1/3 - 1/4
= 24/60 + 20/60 - 15/60=29/60
Two dice are tossed. What are the odds of getting a sum of 7 when two number cubes are tossed?
6/36=1/6 (3,4)(4,3)(2,5)(5,2)(1,6)(6,1)
The probability that Sue will go to Mexico in the winter and to France in the summer is 0.40 . The probability that she will go to Mexico in the winter is 0.60 . Find the probability that she will go to France this summer, given that she just returned from her winter vacation in Mexico.
2/3
Jack had 4 Snicker bars and 8 Mars bars. He randomly chose a piece of candy, ate it, then chose another.
A) Are these events Dependent or Independent?
B) What is the probability that both candy bars were snickers?
A) dependent
B) 4/12 * 3/11=12/132= 1/11
On a spinner labeled with numbers 1-10, where each number is equally likely to be spun, determine the probability of spinning an odd number or a multiple of 3
P(odd) = 5/10
P(multiple of 3) = 3/10
P(odd and multiple of 3)= 2/10
5/10 + 3/10 - 2/10 = 6/10 = 3/5
The probability of two independent events occurring is 1/18. If the probability of one event is 1/3, find the probability of the other event
1/6
P(A and B)= P(A) * P(B)
1/18= 1/3 * x
x= 3/18 or 1/6
You pull out one card from a standard 52 card deck. What is the probability of picking a red card or a three?
26/52+4/52-2/52=28/52=7/13
If the P(A) = .5, P(B) = .6, and P(A or B) = .85, then what is
a) P(A & B)?
b) P(A|B)?
c) P(B|A)?
a) 0.25
b) 5/12
c) 1/2