How do I do these?
1.A number cube is rolled 120 times. The number 4 comes up 47 times. What is the experimental probability of rolling a 4? What is the theoretical probability of rolling a 4?
A)47/120;1/30
B)47/120;1/6
C)4/47;1/6
D)1/6;47/120
2.Food Express is running a special promotion in which customers can win a free gallon of milk with their food
purchase if there is a star on their receipt. So far, 147 of the first 156 customers have not received a star on their receipts. What is the experimental probability of winning a free gallon of milk?
A)11/156
B)49/52
C)2/39
D)3/52
3.A bag containing 5 green marbles, 8 red marbles, 11 orange marbles, 7 brown marbles, and 12 blue marbles. You choose a marble, replace it, and choose again. What is P(red, then blue)?
A)20/43
B)40/43
C)20/1849
D)96/1849
4.You and 5 friends go to a concert. In how many different ways can you sit in the assigned seats?
A)720
B)120
C)30
D)15
1. To find the experimental probability of rolling a 4, you divide the number of times the desired outcome occurred (in this case, rolling a 4) by the total number of trials (in this case, the number of times the number cube is rolled). So for this question, the experimental probability of rolling a 4 is 47/120.
To find the theoretical probability of rolling a 4, you need to determine the number of favorable outcomes (rolling a 4) divided by the number of possible outcomes. With a number cube, there are 6 possible outcomes (numbers 1-6) for each roll. Since there is only one favorable outcome (rolling a 4), the theoretical probability of rolling a 4 is 1/6.
Therefore, the correct answer is A) 47/120; 1/30.
2. The experimental probability of winning a free gallon of milk can be found by dividing the number of times the desired outcome occurred (in this case, receiving a star on the receipt) by the total number of trials (in this case, the number of customers).
From the information given, we know that out of the first 156 customers, 147 did not receive a star on their receipts. So the experimental probability of winning a free gallon of milk is 9/156.
Therefore, the correct answer is not provided in the options given. The correct answer is 9/156.
3. To find the probability of choosing a red marble and then a blue marble, you need to multiply the individual probabilities of both events.
The probability of choosing a red marble on the first draw is 8/43 because there are 8 red marbles out of a total of 43 marbles in the bag.
After replacing the first marble, the probability of choosing a blue marble on the second draw is 12/43 because there are now 12 blue marbles out of a total of 43 marbles.
To find the probability of both events occurring, you multiply the probabilities: (8/43) * (12/43) = 96/1849.
Therefore, the correct answer is D) 96/1849.
4. The number of different ways you and your friends can sit in the assigned seats can be determined using the concept of permutations. In this case, there are 6 people (including yourself) and 6 seats. The number of ways to arrange 6 people in 6 seats is 6 factorial (6!), which is equal to 720.
Therefore, the correct answer is A) 720.