Final answer:
The probability of a student wanting a candy bar or a pencil can be found by adding the individual probabilities and subtracting the probability of wanting both. The probability of wanting neither a candy bar nor a pencil is the complement of wanting a candy bar or a pencil.
Step-by-step explanation:
To find the probability that a randomly chosen student would want a candy bar or a pencil, we need to add the individual probabilities of wanting a candy bar and wanting a pencil and subtract the probability of wanting both.
Let's denote the probability of wanting a candy bar as P(candy bar) and the probability of wanting a pencil as P(pencil).
From the given information, we have:
- P(candy bar) = 32/71
- P(pencil) = 25/71
- P(both) = 4/71
Therefore, the probability of wanting a candy bar or a pencil (P(candy bar or pencil)) is:
P(candy bar or pencil) = P(candy bar) + P(pencil) - P(both) = 32/71 + 25/71 - 4/71 = 53/71.
Hence, the probability that the student chosen would want a candy bar or a pencil is 53/71.
To find the probability that the student chosen would want neither a candy bar nor a pencil, we need to find the complement of the probability of wanting a candy bar or a pencil.
The complement of P(candy bar or pencil) is 1 - P(candy bar or pencil).
So, the probability of wanting neither a candy bar nor a pencil (P(neither)) is:
P(neither) = 1 - P(candy bar or pencil) = 1 - 53/71 = 18/71.