Question

You randomly select two poker chips from a bag containing 7 poker chips: 3 red, 2 green, 1 blue, and 1 white. Compute the following events: Event A: You select a green poker chip Event B: You select t

Answer 1

1. Event A: The probability of selecting a green poker chip is
`\((2)/(7)\).`

2. Event B: The probability of selecting two poker chips of different colors is
`\((24)/(42)\),` which simplifies to
`\((4)/(7)\)`.

Step-by-step explanation:

In Event A, there are 2 green chips out of a total of 7 chips in the bag. Therefore, the probability of selecting a green poker chip is given by the ratio of the number of favorable outcomes to the total number of outcomes, which is
`\((2)/(7)\).`

For Event B, we need to consider the ways of selecting two chips of different colors. There are four combinations: red-green, red-blue, red-white, and green-blue. The total number of ways to select two chips is \
`(\binom{7}{2} = 21\)`, as there are 7 chips, and we want to choose 2. Out of these, 4 combinations satisfy the condition. Therefore, the probability of selecting two chips of different colors is
`\((4)/(21)\)`, which can be simplified to
`\((4)/(7)\).`

To calculate this, we first find the total number of combinations and then determine the number of combinations that meet the criteria. The probability is then expressed as the ratio of favorable outcomes to total outcomes. In this case, the probability of Event
`B is \((4)/(7)\),` indicating a 4 in 7 chance of selecting two chips of different colors from the bag.