Question

(d) experiment 4: a bag contains numbered marbles. a marble is randomly selected from the bag and put back. the marbles are mixed. then another random selection is made.
event a: the first selection is marble number 2.
event b: the second selection is marble number 5.
determine whether events a and b are independent or dependent.
independent dependent
(e) experiment 5: a grocery shelf contains boxes of corn cereal and wheat cereal. hong randomly selects a box of cereal and puts it into his shopping cart. then another random selection is made from the remaining boxes.
event a: the first selection is a box of corn cereal.
event b: the second selection is a box of wheat cereal.
determine whether events a and b are independent or dependent.
independent dependent

Explanation:

• For Experiment 4:
• When a marble is selected and put back (replaced), the probability of selecting marble number 5 in the second draw (Event B) is not affected by the first draw (Event A). The composition of the bag remains the same for both draws.
• For Experiment 5:
• When a box of corn cereal is selected and not replaced (put into the cart), the number of total boxes and the number of wheat - cereal boxes change for the second draw. So, the probability of selecting a box of wheat cereal (Event B) is affected by the first selection (Event A).

Answer:

• (d) Independent
• (e) Dependent