A bag of marbles has equal numbers of red (R), purple (P), blue (B), and orange (O) marbles. A marble is picked from the bag and replaced, then a second marble is picked. Complete parts a and b.
a. Represent the possible outcomes in the sample space. Choose the correct answer below.
Click here to view sample space a.
Click here to view sample space c.
Click here to view sample space d.
Click here to view sample space b.
To find the sample space for this scenario, where you are picking marbles from a bag containing equal numbers of red (R), purple (P), blue (B), and orange (O) marbles, we need to consider all the possible outcomes for the two picks.
Since each time a marble is picked, it is replaced, the outcomes for each pick are independent. Thus, the possible outcomes when picking two marbles can be represented as ordered pairs.
Here are the possible combinations when picking two marbles:
1. RR (red first, red second)
2. RP (red first, purple second)
3. RB (red first, blue second)
4. RO (red first, orange second)
5. PR (purple first, red second)
6. PP (purple first, purple second)
7. PB (purple first, blue second)
8. PO (purple first, orange second)
9. BR (blue first, red second)
10. BP (blue first, purple second)
11. BB (blue first, blue second)
12. BO (blue first, orange second)
13. OR (orange first, red second)
14. OP (orange first, purple second)
15. OB (orange first, blue second)
16. OO (orange first, orange second)
So, the complete sample space consists of 16 outcomes: { RR, RP, RB, RO, PR, PP, PB, PO, BR, BP, BB, BO,