Abiased die has a probability of 1/4 of showing a 5, while the probability of any of 1, 2, 3, 4, or 6 turning up is the same . if three such dice are rolled, what is the probability of getting a sum of at least 14 without getting a 6 on any die ?
option 1 : 5/24
option 2 : 9/160
option 3 : 1/30
option 4 : 7/160

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

The number if marbles of different colors stored in a hat is listed below: 4 red marbles 10 green marbles 7 blue marbles. without looking in the hat, dan takes out a marble at random. he replaces the marble and then takes out another marble from the hat. what is the probability that dan takes out a blue marble in both draws?

Which of the following is the result of expanding