A golf ball is selected at random from a golf bag. If the bag contains 3 black balls, 8 orange balls, and 4 brown balls, find the probability of the event. That the golf ball will be black or orange.
How many are "succesful picks", and how many in total?
To find the probability of the event that the golf ball will be black or orange, we first need to determine the total number of balls in the bag. In this case, the bag contains 3 black balls, 8 orange balls, and 4 brown balls. So, the total number of balls in the bag is:
3 (black balls) + 8 (orange balls) + 4 (brown balls) = 15 balls in total.
Next, we determine the number of black or orange balls in the bag. Since we are considering both black and orange balls, we add their individual counts:
3 (black balls) + 8 (orange balls) = 11 balls.
Therefore, the number of black or orange balls is 11.
Now, we can calculate the probability of the event:
Probability = Number of favorable outcomes / Total number of outcomes.
Number of favorable outcomes (black or orange balls) = 11 balls.
Total number of outcomes (balls in the bag) = 15 balls.
So, the probability of the event that the golf ball will be black or orange is:
11 / 15 ≈ 0.733.
Therefore, the probability is approximately 0.733 or 73.3%.