Question

math 10pre - ib probability quiz #1
name jeremy

1. a machine produces batteries. as part of a quality control process, six batteries are randomly selected every hour and tested. the number of defective batteries is noted.

a) list the sample space.
b) list the following events as subsets of the sample space:
i) at least two batteries are defective ii) at most two batteries are defective
c) list the complement of the following events as subsets of the sample space:
i) three batteries are defective ii) at most five batteries are defective

1. eight coins are tossed and the number of tails is counted.

a) list the sample space.
b) list the event \more tails than heads\ in terms of the sample space.
c) list the event \more heads than tails\ in terms of the sample space.
d) list the complement of the following events as subsets of the sample space:
i) an even number of tails ii) at least one tail

Explanation:

Question 1

Part (a)

Step 1: Determine possible defective counts

When testing 6 batteries, the number of defective batteries can be 0, 1, 2, 3, 4, 5, or 6.

Step 2: Define the sample space

The sample space \( S \) is the set of all possible number of defective batteries. So \( S=\{0, 1, 2, 3, 4, 5, 6\} \).

Step 1: Interpret "at least two"

"At least two" means 2 or more defective batteries.

Step 2: List the subset

From the sample space, the subset for at least two defective batteries is \( \{2, 3, 4, 5, 6\} \).

Step 1: Interpret "at most two"

"At most two" means 2 or fewer defective batteries (0, 1, or 2).

Step 2: List the subset

From the sample space, the subset for at most two defective batteries is \( \{0, 1, 2\} \).

Answer:

\( S = \{0, 1, 2, 3, 4, 5, 6\} \)

Part (b) (i)