Question

Ella created a board game that instructs players to roll a standard 6-sided number cube and pick a marble out of a bag without looking. On Colin's turn, the bag contains 1 red marble, 1 blue marble, and 1 green marble. If Colin can win the game by either rolling a "6" or choosing the red marble, what is the probability that Colin wins the game?

Answer 1

The probability of rolling a 6 is 1/6 .

The probability of pulling the red marble is 1/3 .

The probability of one OR the other is (1/6 + 1/3)

= (1/6 + 2/6)

= 3/6 = 1/2 (50%)

Answer 2

Answer: The required probability that Colin wins is 50%.

Step-by-step explanation: Given that Ella created a board game that instructs players to roll a standard 6-sided number cube and pick a marble out of a bag without looking.

On Colin's turn, the bag contains 1 red marble, 1 blue marble, and 1 green marble.

We are to find the probability that Colin wins the game if he can win the game by either rolling a "6" or choosing the red marble.

Let S denote the sample space for the experiment of rolling a die and A denote the event of rolling a 6.

Then, n(S) = 6 and n(A) = 1.

Again, let S' denote the sample space for the experiment of selecting a marble from the bag with 1 red marble, 1 blue marble and 1 green marble

and B denote the event of selecting a red marble.

Then, n(S') = 3 and n(B) = 1.

Therefore, the probability that Colin wins the game will be

`P(A)+P(B)\\\\\\=(n(A))/(n(S))+(n(B))/(n(S'))\\\\\\=(1)/(6)+(1)/(3)\\\\\\=(3)/(6)\\\\\\=(1)/(2)*100\%\\\\=50\%.`

Thus, the required probability that Colin wins is 50%.