Question

Two dance teams, the Roses and the Tulips, are perfectly matched so that their chances of winning are both set at 50%. What is the probability that the Roses will win the next 3 out of 4 games? Round the answer to the nearest whole percent. (No decimals)

Answer 1

6%

Explanation:

Step 1

The fist step is to define the probabilities.

The events are independent from each other. Each team wins with probability
`(1)/(2)` and looses with probability
`(1)/(2).` Let
`P(W_R)` be probability that Roses win and
`P(L_R)` be the probability that Roses loose.

Step 2

The second step is to calculate the probabilities by multiplying the probabilities with the first 3 terms in the product being the probability of a win and the last term being the probability of a loss.

The calculation is shown below,

`P(W_R)* P(W_R)* P(W_R)* P(L_R)=(1)/(2) * (1)/(2) *(1)/(2) *(1)/(2) =(1)/(16)`

Step 3

The last step is to convert this probability into a percentage. Converting this probability to a percentage is done as shown below,

`(1)/(16) * 100\%=6.25\%.`

Step 4

The next step is to round down the percentage . The value of 6.25% rounded down is 6%. The correct answer is 6%.