Final answer:
The probability that an item chosen at random from the postbox is both first class and a parcel (P(first class and parcel)) is 2/35.
Step-by-step explanation:
To calculate the probability of choosing an item that is both first class and a parcel (P(first class and parcel)), we can use the information given and structure it in a frequency tree. There are 70 items in total, with 36 being sent first class. Out of these 36 first-class items, we need to find out how many are parcels.
The question also states that there are 10 parcels in total. We also know that there are 28 items which are neither parcels nor first class. This means that the remaining items are either a parcel, first class, or both. With this information, we can deduce that there must be 70 - 28 = 42 items that are either parcels or first class.
Since we know there are 10 parcels and 36 first-class items, we can find the number of first-class parcels by considering that some of the parcels are part of the 36 first-class items. This overlap can be calculated as follows:
- Total parcels or first class items: 42
- First-class items: 36
- Parcels: 10
- Overlap (first-class parcels): 36 + 10 - 42 = 4
Thus, 4 of the items are both first class and parcels. Therefore, the probability of choosing an item that is both first class and a parcel is:
P(first class and parcel) = Number of first class parcels / Total number of items = 4 / 70
In simplest form, this fraction is 2/35.