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. For the first question, to find the experimental probability of rolling a 4, you need to divide the number of times the event occurs by the total number of trials. In this case, the number 4 comes up 47 times out of 120 rolls. So 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 total number of possible outcomes (rolling any number from 1 to 6). The number of favorable outcomes is 1 (as there is only one 4 on a number cube) and the total number of possible outcomes is 6. Therefore, the theoretical probability of rolling a 4 is 1/6.
So, the answer to the first question is B) 47/120; 1/6.
2. In the second question, to find the experimental probability of winning a free gallon of milk, you need to divide the number of successful outcomes (customers who received a star on their receipt) by the total number of trials (number of customers). In this case, 147 customers did not receive a star out of the first 156 customers. So the experimental probability of winning a free gallon of milk is (156-147)/156 = 9/156 = 3/52.
Therefore, the answer to the second question is D) 3/52.
3. In the third question, to find the probability of selecting a red marble, replacing it, and then selecting a blue marble, you need to multiply the individual probabilities of each event.
The probability of selecting a red marble is 8/43 (since there are 8 red marbles out of 43 total marbles).
The probability of selecting a blue marble is 12/43 (since there are 12 blue marbles out of 43 total marbles).
Therefore, the probability of selecting a red marble, replacing it, and then selecting a blue marble is (8/43) * (12/43) = 96/1849.
So, the answer to the third question is D) 96/1849.
4. In the fourth question, to find the number of different ways you can sit in the assigned seats, you need to use the permutation formula. The total number of people (including yourself) is 6.
The number of ways to arrange n distinct objects in a line is given by n!. In this case, 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.
Therefore, the answer to the fourth question is A) 720.
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3. If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.