A bag contains 7 green marbles and 4 white marbles. You select a marble at random. What are the odds in favor of picking a green marble?
The probability of picking a green marble is 7/11.
The odds in favor of an event happening are defined as the ratio of the probability of the event happening to the probability of the event not happening.
So, the odds in favor of picking a green marble can be calculated as:
(Probability of picking a green marble) / (Probability of picking a white marble)
= (7/11) / (4/11)
= 7/4
Therefore, the odds in favor of picking a green marble are 7 to 4.
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, 219 of the first 264 customers have not received a star on their receipts. What is the experimental probability of winning a free gallon of milk?
To find the experimental probability of winning a free gallon of milk, we need to know how many of the first 264 customers received a star on their receipt.
Number of customers who received a star = Total customers - Customers who did not receive a star
Number of customers who received a star = 264 - 219
Number of customers who received a star = 45
Therefore, out of the first 264 customers, 45 received a star on their receipt.
The experimental probability of winning a free gallon of milk is the ratio of the number of customers who received a star to the total number of customers.
Experimental probability = Number of customers who received a star / Total customers
Experimental probability = 45 / 264
Experimental probability = 0.17 (rounded to two decimal places)
So, the experimental probability of winning a free gallon of milk is 0.17 or 17%.
A bag contains 7 green marbles, 9 red marbles, 10 orange marbles, 5 brown marbles, and 10 blue marbles. You choose a marble, replace it, and choose again. Find P(red, then blue).
The probability of selecting a red marble on the first draw is 9/41 (since there are 9 red marbles out of a total of 41 marbles in the bag).
After replacing the red marble in the bag, the probability of selecting a blue marble on the second draw is also 10/41 (since there are still 10 blue marbles out of a total of 41 marbles).
To find the probability of both events happening (selecting a red marble and then a blue marble), we multiply their probabilities:
P(red, then blue) = P(red) * P(blue|red)
P(red, then blue) = (9/41) * (10/41)
P(red, then blue) = 90/1681
P(red, then blue) = 0.0535 (rounded to four decimal places)
Therefore, the probability of selecting a red marble, replacing it, and then selecting a blue marble is approximately 0.0535.
To find the odds in favor of picking a green marble, we need to determine the favorable outcomes (picking a green marble) and the total outcomes (picking any marble, either green or white).
Favorable outcomes: There are 7 green marbles in the bag.
Total outcomes: There are 7 green marbles + 4 white marbles = 11 total marbles in the bag.
Therefore, the odds in favor of picking a green marble can be written as:
Favorable outcomes : Total outcomes
7 : 11
To find the odds in favor of picking a green marble, you need to determine the number of favorable outcomes (green marbles) and the total number of possible outcomes (all marbles).
Given that the bag contains 7 green marbles and 4 white marbles, the total number of possible outcomes is the sum of the green and white marbles, which is 7 + 4 = 11.
The number of favorable outcomes, in this case, is the number of green marbles, which is 7.
Therefore, the odds in favor of picking a green marble can be expressed as a ratio of the number of favorable outcomes to the total number of possible outcomes, which is 7/11.
So, the odds in favor of picking a green marble are 7 to 11, or 7:11.