brvedwinner
Answered

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 :

AL2006

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:  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

[tex]P(A)+P(B)\\\\\\=\dfrac{n(A)}{n(S)}+\dfrac{n(B)}{n(S')}\\\\\\=\dfrac{1}{6}+\dfrac{1}{3}\\\\\\=\dfrac{3}{6}\\\\\\=\dfrac{1}{2}\times100\%\\\\=50\%.[/tex]

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

Other Questions