Question

you and a friend decide to go fishing. since you are fishing for sport, you throw back whatever you catch. the pond is stocked with 2 different type of fish: 3 sunfish, 1 carp. event 1 (e1): catch a fish. event 2 (e2): catch a second fish. determine the sample space using a table. assume the events are random. enter the outcomes of taking both actions in the blank cells of the table. then fill in the probability below. p(the same type of fish) =

Explanation:

Step1: Define sample space pairs

Each cell is an ordered pair (E1 outcome, E2 outcome)

Step2: Fill first row (E1=sunfish)

$(s,s), (s,s), (s,s)$

Step3: Fill second row (E1=sunfish)

$(s,s), (s,s), (s,s)$

Step4: Fill third row (E1=sunfish)

$(s,s), (s,s), (s,s)$

Step5: Fill fourth row (E1=carp)

$(c,s), (c,s), (c,s)$

Step6: Count total outcomes

Total outcomes = $4 \times 3 = 12$

Step7: Count same-type outcomes

Same-type outcomes: all (s,s) pairs = $3 \times 3 = 9$

Step8: Calculate probability

$P(\text{same type}) = \frac{\text{Same-type outcomes}}{\text{Total outcomes}} = \frac{9}{12} = \frac{3}{4}$

Answer:

Filled Table:

Event 1 Outcomes	Event 2 Outcomes: sunfish (s)	Event 2 Outcomes: sunfish (s)	Event 2 Outcomes: sunfish (s)
sunfish (s)	$(s,s)$	$(s,s)$	$(s,s)$
sunfish (s)	$(s,s)$	$(s,s)$	$(s,s)$
carp (c)	$(c,s)$	$(c,s)$	$(c,s)$

Probability:

$\frac{3}{4}$