A bag contains 100 bolts and 300 nuts 50% of each have been rusted 1 item is chosen at random.
Find the probability that chosen item z rusted or a bolt.
To find the probability that the chosen item is either rusted or a bolt, we need to calculate the probability of each event separately and then add them together.
Let's start with calculating the probability that the chosen item is rusted.
We know that 50% of the bolts are rusted, which means that 50 bolts out of 100 are rusted.
So, the probability that a chosen item is rusted is 50/400 = 1/8.
Now let's calculate the probability that the chosen item is a bolt.
There are 100 bolts and 400 total items in the bag (100 bolts + 300 nuts).
Therefore, the probability of choosing a bolt is 100/400 = 1/4.
To find the probability that the chosen item is either rusted or a bolt, we add the probabilities of the two events:
1/8 + 1/4 = 1/8 + 2/8 = 3/8.
Therefore, the probability that the chosen item is either rusted or a bolt is 3/8.
To find the probability of choosing a rusted item or a bolt, we first need to determine the number of items that satisfy either of these conditions.
There are 100 bolts and 300 nuts in the bag. Since 50% of each have been rusted, we can determine the number of rusted items as follows:
Number of rusted bolts = 0.50 * 100 = 50
Number of rusted nuts = 0.50 * 300 = 150
To calculate the probability of choosing a rusted item or a bolt, we need to add the number of rusted bolts to the number of non-rusted bolts, as well as the number of rusted nuts to the number of non-rusted nuts.
Number of non-rusted bolts = 100 - 50 = 50
Number of non-rusted nuts = 300 - 150 = 150
Therefore, the total number of items that satisfy the conditions (rusted item or a bolt) is:
Number of rusted items or bolts = Number of rusted bolts + Number of non-rusted bolts
= 50 + 50 = 100
The total number of items in the bag is 100 + 300 = 400.
Finally, we can calculate the probability by dividing the number of items that satisfy the conditions by the total number of items:
Probability = Number of rusted items or bolts / Total number of items
= 100 / 400
= 0.25
Therefore, the probability of choosing a rusted item or a bolt is 0.25 or 25%.
200/400 = probability of finding rusted object.
100/400 = probability of choosing a bolt
Either-or probability found by adding individual probabilities.