An experiment consists of rolling a die and selecting a marble from a bag. the bag has 7 orange, 3 pink, and 6 grey marbles. What is the probability of rolling a multiple of 3 and selecting a pink marble?
Anwer: The two events are independent of each other, therefore we multiply.
For multiple of 3: 1/6 + 1/6 = 1/3
P(E and F)=P(E)*P(F)
= 1/3 * 3/16
=1/16
Can some please check my answer to make sure it is correct?
Thanks
To find the probability of rolling a multiple of 3 and selecting a pink marble, you correctly stated that we need to multiply the probabilities of the two events since they are independent.
First, let's calculate the probability of rolling a multiple of 3. A die has 6 sides, and only two of them (3 and 6) are multiples of 3. So, the probability of rolling a multiple of 3 is 2/6 = 1/3.
Next, we need to calculate the probability of selecting a pink marble from the bag. There are a total of 7 + 3 + 6 = 16 marbles in the bag, and 3 of them are pink. Therefore, the probability of selecting a pink marble is 3/16.
Now, we can multiply the probabilities of the two events: (1/3) * (3/16) = 1/48.
So, the correct answer is 1/48.
Hope this clarifies the solution for you!