In a random sample of bags of candy, it was found that 47% of pieces contained chocolate. It was also found that of those pieces that contained chocolate, 27% contained nuts. Of the pieces of candy that did not have chocolate, 7% contained nuts.
Let C be the event that the candy contained chocolate and N be the event that the candy contained nuts. Find the following probabilities. Enter your answers as either decimals or fractions (not percentages).
P(C_)
P(C) = 47% = 0.47
To find the probability of an event not occurring, we can use the complement rule, which states that the probability of an event not happening is 1 minus the probability of the event happening.
In this case, we want to find the probability of candy not containing chocolate, denoted as P(C'). To calculate this, we subtract the probability of candy containing chocolate (P(C)) from 1.
P(C') = 1 - P(C)
Given that 47% of candy contains chocolate, we have:
P(C) = 47% = 0.47
Thus,
P(C') = 1 - P(C) = 1 - 0.47 = 0.53
Therefore, the probability of a bag of candy not containing chocolate is 0.53 or 53/100.
To find the probability of an event, we need to divide the number of favorable outcomes by the total number of possible outcomes. In this case, we want to find the probability that candy does not contain chocolate, represented as P(C').
Given that 47% of candy pieces contain chocolate, we know that the probability of a candy piece containing chocolate is 0.47. Therefore, the probability of a candy piece not containing chocolate can be calculated by subtracting this value from 1.
P(C') = 1 - P(C)
P(C') = 1 - 0.47
P(C') = 0.53
So, the probability of a candy piece not containing chocolate is 0.53 or 53/100.