Question

Suppose a jar contains 7 red marbles and 18 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

63

Explanation:

we divided 18÷2=9

and we multiply 9×7=63

Answer 2

`p(a) = (7)/(100)`

Explanation:

Given:

7 red marbles

18 blue marbles

Total number of marbles: 7 + 18 = 25

All outcomes:

`n = (25 * 24)/(2 * 1) = 300`

• 25 × 24, because the first marble can be pulled out in 25 ways, and the second marble - in 24 ways, since the first one has already been pulled out.
• We divide by the factorial of 2, because the order does not matter how we pull out the marbles

Let's name the event A:

A - "both marbles are red"

Event's A favorable outcomes:

`m(a) = (7 * 6)/(2 * 1) = 21`

• 7 × 6, because we only need to pull the red marbles out, so there are 7 ways to pull out the 1st marble and 6 ways for the 2nd one to be pulled out (the order doesn't matter)

`p(a) = (m(a))/(n) = (21)/(300) = (7)/(100)`