(odds) Playing Bingo:When playing bingo, 75 balls are placed in a bin and balls are selected at random. Each ball is marked with a letter and a number as indicated in the following chart: B: 1-15
I: 16-30 N:31-45 G:46-60 O:61-75. For example there are balls marked B1,B2 up to B15; I16, I17, up to 30 and so on. Assuming one bingo ball is selected at random, determine the probability that it does not contain the letter G.
To determine the probability that a randomly selected bingo ball does not contain the letter G, we need to find out how many balls do not contain the letter G and divide it by the total number of balls.
Step 1: Find the number of balls that do not contain the letter G.
In the given chart, the letter G represents numbers from 46 to 60. So, the number of balls without the letter G is the sum of the balls in the letters B, I, N, and O.
Number of balls without the letter G = Number of balls in B + Number of balls in I + Number of balls in N + Number of balls in O
Number of balls without the letter G = (15 balls in B) + (15 balls in I) + (15 balls in N) + (15 balls in O)
Number of balls without the letter G = 15 + 15 + 15 + 15 = 60
Step 2: Find the total number of balls.
The total number of balls in the bin is given as 75.
Step 3: Calculate the probability.
Probability = Number of favorable outcomes / Total number of outcomes
Here, the favorable outcome is selecting a ball without the letter G, which is 60.
Probability = 60 / 75
Probability = 4 / 5
Probability = 0.8
So, the probability that a randomly selected bingo ball does not contain the letter G is 0.8 or 80%.
To determine the probability that a randomly selected bingo ball does not contain the letter G, we need to find out the total number of balls that do not contain the letter G, as well as the total number of balls in the bin.
From the given information, we know that the letter G is assigned to the numbers 46-60. Therefore, there are 60-45+1 = 16 balls marked with the letter G.
To find the total number of balls in the bin, we sum up the number of balls for each letter:
B: 15 balls
I: 15 balls
N: 15 balls
G: 16 balls
O: 15 balls
So, the total number of balls in the bin is 15+15+15+16+15 = 76.
To calculate the probability that a randomly selected bingo ball does not contain the letter G, we divide the number of balls that do not contain G (60) by the total number of balls in the bin (76):
P(not containing G) = 60/76 = 0.7895 (rounded to four decimal places)
Therefore, the probability that a randomly selected bingo ball does not contain the letter G is approximately 0.7895 or 78.95%.