independent and dependent events
A coin is tossed and a six-sided die is rolled. Find the probability of getting ahead on the coin and 6 on the die
p(heads)=½
P(6)=⅙
P (A+B)= P(A) * P(B)
= ½ * ⅙ = 1/12
Which of the following cannot be a probability of an event?
a.2/3
b.0
c.−1.5
d.1/2
c.-1.5
Q1) Find the Experimental Probability in a Throw of Dice of a) Obtaining a Four, b) Obtaining a Number Less Than 5
In a throw of a dice, we get the outcomes out of 1, 2, 3, 4, 5, and 6. Now, we will proceed one by one for our desired outcomes.
We know that the Experimental probability is calculated by the formula: Number of times an event occurs/Total number of trials
a) Obtaining a 4 : 14/80= 0.175 or 17.5%
b) Rolling a number less than 4: Outcomes are 1, 2, and 3. The frequency of each is 13, 10, and 15. Now, sum up these all you get the number of times an event occurred, i.e., 38.
P (numbers less than 4) = 38/80 = 0.475 or 47.5%
If a six-faced cube is rolled once (numbered the faces from 1 to 6), find the probability of getting an even number.
All possible outcomes = {1, 2, 3, 4, 5, 6}
Number of all possible outcomes : 6
Possible outcomes for an even number = {2, 4, 6}
Number of favorable outcomes : 3
ratio= number of favorable outcomes/number of possible outcomes
Ratio = 3/6
Ratio = 0.5
Hence, the probability of getting an even number is 0.5 or 50%.
9*23
207
Yalena has to select two students from a class of 22 girls and 24 boys. What is the probability that both students chosen are boys?
Total number of students = 22 + 24 = 46
Probability of choosing the first boy, say Boy 1 = 24/48
Probability of choosing second boy, say Boy 2 = 23/47
Now,
P(Boy 1 and Boy 2) = P(Boy 1) and P(Boy 2|Boy 1)
= 24/48 23/47
= 552/2256
Julian is trying to understand mutually exclusive events using a dice. Help Julian understand what is the probability of a dice showing 2 or 4?
There are a total of 6 faces on a die, hence, the total number of outcomes will be 6
The probability of a die showing 2 is P(2) = 1/6
The probability of a die showing 4 isP(4) = 1/6
The probability of getting 2 or 4 is = P(2 or 4)
= P(2 or 4)
= P (2) + P(4)
= (1/6) + (1/6)
= 1 + 1/ 6
= 2/6
= 1/3
Which of the Following is an Experimental Probability?
Options:
17/11
- 0.32
2.4
65%
Option (4): Experimental probability expressed in terms of percentage has a value lying between 0 and 1
A bag contains 6 blue balls, 4 yellow balls, and 2 red balls.
What is the theoretical probability of getting a yellow ball?
Since you have 4 yellow balls playing on your favor, the number of favorable outcomes is 4.
To get the number of possible outcomes, just count all the balls. Number of possible outcomes is 12.
probability of getting a yellow ball =
4/12
probability of getting a yellow ball = 0.3333
probability of getting a yellow ball = 33.33%
590*6(5+5)
35400
In a survey found that 8 out of 12 people walk to the office. 2 persons are selected randomly. What is the probability that all two walk to the office?
The probability that both walk to the office = 2/12 * 2/12 * 1/11 = 4/1584
Caroline noticed her mother trying to take out the fish to clean the fish tank. She asked her mother, "How many are males and how many are females?" Her mother replied that the tank contained 5 male fish and 8 female fish. What is the probability that the fish her mother takes out first is a male fish?
Probability of an event = Number of possible outcomes/ Total no of favorable outcomes
No. of male fish = 5
No. of female fish = 8
Total no of fishes
5+8 = 13
The probability that the fish are taken out is a male fish: No of male fish/ Total no of fishes
The probability that the fish are taken out is a male fish 5/13
Answer: Probability is 5/13.
A manufacturer makes 50,000 cell phones every month. After inspecting 1000 phones, the manufacturer found that 20 phones are defective. What is the probability that you will buy a phone that is defective? Predict how many phones will be defective next month.
EP = 20/1000 = 0.02
0.02 = 2/100 = 2%
The probability that you will buy a defective phone is 2%
Number of defective phones next month = 2% × 50000
Number of defective phones next month = 0.02 × 50000
Number of defective phones next month = 1000
Throw a die once. What is the probability of getting a number less than 6?
Ask yourself, "How many number are less than 6?"
Since there are 5 numbers less than 6, the number of favorable outcomes is 5.
Since the die had a total of 6 numbers, the number of possible outcomes is 6.
probability of getting a number less than 6 = 56
probability of getting a number less than 6 =0.8333.
probability of getting a number less than 6 =83.33%
This means that it is very likely you will get a number less than 6.
In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
10 students are 10 years old
A bag has 4 red, 6 blue, and 3 yellow balls. 2 balls are drawn, but the first ball is drawn without replacement. Find the following.
a] P (red, then blue)
b] P (blue, then blue)
There are four red balls and a total of thirteen balls.
P (red) = 6 / 13
The probability of the second draw affected the first.
Number of blue balls = 6
Total number of balls left = 12
P (drawing blue after red) = 5 / 12
P(drawing red, then blue) = P (drawing red) * P (blue after red) =
1/ 4 will be the probability value of drawing a red ball followed by a blue ball.
b] Number of blue balls = 3
Total number of balls left = 13
The probability of drawing a blue ball = 5 / 13
The probability of the second draw affected the first.
Now there are 6 blue balls left and a total of 13 balls left.
P (drawing a blue ball after a blue ball) = 4 / 13
P (blue, then blue) = P (drawing blue ball) * (drawing a blue ball after a blue ball) =
Hence, the probability of drawing a red ball followed by a blue ball is 4 / 21.
The probabilities of three mutually exclusive events are given as 1/ 6, 2/3, and 1/4. Prove whether the given statement is correct or not.
Let the events be X, Y and Z
If the events are mutually exclusive, then X ∩ Y = Θ , Y ∩ Z= Θ and X ∩ Z = Θ
If the conditions given above are satisfied , then P ( X ∪Y ∪ Z) = P(X) + P(Y) + (Z)
Since, P( X ∪ Y ∪ Z) = 13/12 > 1, the probability values comes within 1
so, the statement is incorrect.
There are about 319 million people living in the USA. Pretend that a survey of 1 million people revealed that 300,000 people think that all cars should be electric. What is the probability that someone chosen randomly does not like electric car? How many people like electric cars?
700000/1000000 = 0.7
0.3 = 70/100 = 70%
The probability that someone chosen randomly does not like electric car is 70%
Probability that someone like electric cars is
300000/1000000= 0.3
Let x be the number of people who love electric cars
x = 0.3 × 319 million
x = 95.7 million
In a bag there are 5 green balls, 9 blue balls and 6 red balls. What is the probability of choosing a blue ball?
9/2
what is the formula for finding a circumference
C = 2*pi* r
In a shipment of 22 computers, 4 are defective. Four computers are randomly selected and tested. What is the probability that all four are defective if the first and second ones are not replaced after being tested?
4/22 * 3/21 * 2/20= 24/9240 = 1/386
A box containing 4 bulbs, the probability of having one defected bulb is 0.5 and the probability to have zero defected bulb is 0.4. Calculate the probability of one defected bulb and zero defected bulb.
Probability of single bulb being defected is P(X) =0.5
Probability of zero bulbs being defected is P(Y) = 0.4
As there can be either zero defected bulb or 1 defected bulb because these two events cannot occur simultaneously. Hence, they are considered as mutually exclusive.
P( X or Y) = 0.5 + 0.4 = 0.9
So far, 907of the 1223 voters have agreed to the new amendment.
Based on this data, what is a reasonable estimate of the probability that the next voter does not agree to the new amendment?
a. 316/907
b. 907/1223
c. 1223/2130
d. 316/1223
Choose 1 answer:
d. 316/1223
what is the difference between theoretical and experimental
Experimental probability varies from theoretical probability in that experimental probability is based on real experiment outcomes. The theoretical probability, on the other hand, is based on possible outcomes based on assumptions.
what is a power of product?
The Power of a Product rule basically shows that an expression can be simplified by multiplying the exponents and the numbers that are not exponents stay the same only the exponents multiply.