Dependent or Independent
and The Multiplication Rule
and The Multiplication Rule
You pick a card out from a standard deck and then flip a coin.
What is the probability of picking a red card and then flipping heads?
B) P(AandB)= P(A) * P(B)= 26/52 * 1/2
0.25
Two events that cannot happen simultaneously are...
Mutually Exclusive
A bowl contains four apples, three bananas, three oranges, and two pears. If two pieces of fruit are selected at random, what is the probability of selecting an orange and then a banana?
3/12 * 3/11
0.068
What is the probability of choosing a queen from a deck of 52 cards if a king was already chosen and not replaced?
P(B|A) = 4/51
0.078
Children in a study are split up into preferring chocolate vs preferring vanilla. If the probability of choosing a student who likes vanilla is 0.655, what is the probability of choosing a student who likes chocolate?
P(chocolate) = 1 - 0.655 = 0.345
0.345
The probability of selecting a red marble, not replacing it, then selecting a green marble from a box of 6 red and 2 green marbles
B) Determine the probability
B) 6/8 * 2/7 = 3/14
0.214
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
34% + 56% = 90%
90%
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) = 1/2
0.5
What is the probability of tossing heads on a coin given that you rolled a die and obtained a 5 first?
P(B|A) = 1/2
0.5
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?
B) Determine the probability
A) Not mutually exclusive
B) 4/52 + 26/52 - 2/52 = 28/52 = 7/13
Not Mutually Exclusive, 0.538
You pick a card out of a deck, put it back, then pick another card
Are these events independent or dependent?
Independent
A six-sided die is rolled. Find the probability of rolling an even number or a number greater than 4.
3/6 + 2/6 - 1/6 = 4/6 = 0.667
0.667
What is the probability of rolling an even or a number greater than 4 on a die?
3/6 + 2/6 - 1/6 = 4/6 = 2/3
0.667
A college class has 35 students. 12 are female. What is the probability of randomly selecting a female student to answer a question given that a female student was already asked to answer a question and each student gets one turn to answer per class?
P(B|A) = 11/34
0.324
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?
P(AorB)= P(A) + P(B) - P(AandB)
P(AorB)= 2/5 + 1/3 - 1/4
0.483
You flip a coin and then flip the same coin again.
B) Find the probability of getting two heads
1/2 * 1/2= 1/4
0.25
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 or 4/5
0.8
A bag contains 3 black, 5 green, and 4 yellow marbles.
Two marbles are selected in sequence without replacement. What is the probability of selecting a black marble and then a black marble again?
3/12 * 2/11 = 0.045
0.045
3 red marbles, 4 blue marbles, and 6 orange marbles are in a jar. What is the probability of choosing an orange marble if a blue and an orange marbles were already chosen and not replaced?
P(B|A) = 5/11
0.455
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= 1/11
0.091
The probability of randomly selecting two dimes from a bag containing 10 dimes and 8 pennies if the first selection is replaced
Determine the probability of selecting two dimes
10/18 * 10/18 = 25/81
0.309
The probability of rolling a six-sided die and getting an even OR an odd number.
1
Find the probability of randomly selecting 3 red pencils in sequence, without replacing them, from a box containing 5 red, 3 blue, and 4 green pencils.
5/12 * 4/11 * 3/10 = 0.045
0.045
P(A) = 34% P(A|B) = 53% are the events independent or dependent?
Dependent
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
5/10 + 3/10 - 2/10 = 6/10 = 3/5
0.6