Question

There are five teams in a baseball league. The Astros' probability of winning is1/3. The Cardinals' probability of winning is 1/6, and the Reds' probability of winning is 1/4. The Cubs and the Pirates have the same probability.oftable of probabilities correctly shows the sample space for this situation?

Answer 1

Given that

The Astros' probability of winning is 1/3.

The Cardinals' probability of winning is 1/6.

The Reds' probability of winning is 1/4.

The Cubs and the Pirates have the same probability.

Let x be the probability of Cubs and Pirates.

We know that the sum of all the probabilities is equal to 1.

Adding all the probabilities as follows.

`(1)/(3)+(1)/(6)+(1)/(4)+x+x=1`

`(1)/(3)+(1)/(6)+(1)/(4)+2x=1`

Here LCM of 3,6, and 4 is 12, making the denominator 12.

`(1*4)/(3*4)+(1*2)/(6*2)+(1*3)/(4*3)+2x=1`

`(4)/(12)+(2)/(12)+(3)/(12)+2x=1`

`(4+2+3)/(12)+2x=1`

`(9)/(12)+2x=1`

`(3)/(4)+2x=1`

Adding -3/4 on both sides, we get

`(3)/(4)+2x-(3)/(4)=1-(3)/(4)`

`2x=1-(3)/(4)`
`\text{Use 1=}(4)/(4)\text{ as follows.}`

`2x=(4)/(4)-(3)/(4)`

`2x=(1)/(4)`

Dividing by 2 on both sides, we get

`(2x)/(2)=(1)/(4*2)`
`x=(1)/(8)`

Hence the Cubs' probability is 1/8, and the Pirates' probability is 1/8.

Hence the option 4th is correct.