Question

84 points if someone gets it right.

You randomly draw one marble from this collection.


1 regular marble. 1 checker marble, 3 striped marbles, and 2 bricked marbles.


After that you randomly darw once from this deck of cards. Numbers: 8 3 8 8 3


What is the probability of drawing a checkered marble and then drawing a prime number? Write your answer as a fraction.

Answer 1

First, we have to acknowledge that the marble draw's outcome is independent from the card being drawn. Because of this independence, we can multiply the two individual probabilities.

For the marble, there are 7 outcomes (7 marbles we could draw) and only 1 of which is checkered We have a 1/7 chance of picking a checkered marble.

For the cards, there are 5 possible outcomes (5 cards we could drawa) and 2 are prime (there are two "3" cards). We have a 2/5 chance of drawing a card with a prime number.

For the overall probability, since the two events are independent, we multiply the individual probabilities to find the overall probability:

1/7 · 2/5 = 2/35

We have a 2/35 (about 5.714%) chance of drawing a checkered marble and then picking a card with a prime number.

Answer 2

`(2)/(35)`

Explanation:

`\frac{ \binom{1}{1} }{ \binom{7}{1} } * \frac{ \binom{2}{1} }{ \binom{5}{1} } = (2)/(35)`

of course it can easily be simplified, but the logic is shown here!

first you have to draw 1 checker marble out of the seven marbles.

at the top is the ideal draw where you draw the one checker marble out of that one, and the bottom is all the options to draw 1 marble out of the 7 marbles.

3 is the prime number.

again, at the top you draw obe 3 out of the two, and the bottom is all the options to draw one out of the five numbers.