In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks, villagers can choose either Chai or Lassi.
- (i) List the sample space of all possible snack and drink combinations a person could choose at the fair.
- (ii) List the event ‘Selecting Samosa as a snack.’
Step-by-step solution
Idea: Each outcome is one snack paired with one drink. Go through the snacks one by one and pair each with both drinks. An event is the subset of outcomes that fit its description.
(i) List the sample space of all possible snack and drink combinations a person could choose at the fair.
- Samosa can go with Chai or Lassi; so can Pakora; so can Bhaji. Number of combinations = 3 × 2 = 6.1 mark
- S = {(Samosa, Chai), (Samosa, Lassi), (Pakora, Chai), (Pakora, Lassi), (Bhaji, Chai), (Bhaji, Lassi)}.1 mark
(ii) List the event ‘Selecting Samosa as a snack.’
- Pick the outcomes from S in which the snack is Samosa (with either drink): E = {(Samosa, Chai), (Samosa, Lassi)}.1 mark
Check: 3 snacks × 2 drinks = 6 pairs ✓. The event is a subset of S: both of its outcomes appear in the list.
Answer to write in the exam
(i)
Number of combinations = 3 × 2 = 6
∴ S = {(Samosa, Chai), (Samosa, Lassi), (Pakora, Chai), (Pakora, Lassi), (Bhaji, Chai), (Bhaji, Lassi)}
(ii)
∴ E = {(Samosa, Chai), (Samosa, Lassi)}
Common mistakes that cost marks
- Listing the event as just {Samosa}. The outcomes of this experiment are snack-and-drink pairs, so the event must be written with pairs.
- Listing 5 items {Samosa, Pakora, Bhaji, Chai, Lassi} as the sample space. A person chooses one snack and one drink, so outcomes are pairs.
- Missing a combination such as (Bhaji, Lassi). Work through each snack in turn to be sure all 6 are listed.
How this can come in the exam
A canteen offers 4 kinds of sandwich and 3 kinds of juice. A student picks one sandwich and one juice. The number of possible combinations is
- 7
- 8
- 12
- 16
Show answer
(C) 12
4 × 3 = 12 pairs.
A student chooses one subject from {Music, Art} and one sport from {Chess, Kabaddi, Football}. List the sample space and the event ‘the student chooses Kabaddi’.
Show answer
S = {(Music, Chess), (Music, Kabaddi), (Music, Football), (Art, Chess), (Art, Kabaddi), (Art, Football)}. Event = {(Music, Kabaddi), (Art, Kabaddi)}.Try one yourself
Breakfast is one of {Idli, Dosa} with one of {Sambar, Chutney}. List all combinations and the event ‘choosing Chutney’.
Show answer
S = {(Idli, Sambar), (Idli, Chutney), (Dosa, Sambar), (Dosa, Chutney)}. Event = {(Idli, Chutney), (Dosa, Chutney)}.
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