Question 1186983
Here's how to solve this probability problem.  I'll need the table of outcomes and probabilities to give you specific numerical answers.  However, I will show you the general method.  *Please provide the table so I can complete the calculations.*

**General Method and Explanation:**

Let's represent the different head sizes as M (midsized), O (oversized), and E (extra-oversized), and the grip sizes as S (small), M (medium), and L (large).  The table would look something like this (but with actual probabilities):

| Outcome (Head, Grip) | Probability |
|---|---|
| (M, S) | P(M, S) |
| (M, M) | P(M, M) |
| (M, L) | P(M, L) |
| (O, S) | P(O, S) |
| (O, M) | P(O, M) |
| (O, L) | P(O, L) |
| (E, S) | P(E,S) |
| (E,M) | P(E,M) |
| (E,L) | P(E,L) |

*Remember: The sum of all probabilities must equal 1.*

**a) P(A): Grip size of 1/4 inch**

Event A corresponds to all outcomes where the grip size is 1/4 inch (which I'm assuming is represented by "S" for small in my example).

P(A) = P(M, S) + P(O, S) + P(E,S)

*Interpretation:*  P(A) is the probability that a randomly selected customer purchased a racket with a small (1/4 inch) grip.

**b) P(Aᶜ):**

P(Aᶜ) = 1 - P(A)  (This is the complement of event A; the probability that the grip size is *not* 1/4 inch).

**c) P(B): Oversized head**

Event B corresponds to all outcomes where the head size is oversized (O).

P(B) = P(O, S) + P(O, M) + P(O, L)

**d) Grip size at least 1/2 inch**

"At least 1/2 inch" means medium (M) or large (L) grip sizes.

P(grip ≥ 1/2) = P(M, M) + P(M, L) + P(O, M) + P(O, L) + P(E,M) + P(E,L)

**e) Grip size 1/4 inch and oversized head**

This is the probability of the intersection of events A and B.

P(A ∩ B) = P(O, S)

**f) Grip size 1/4 inch or oversized head**

This is the probability of the union of events A and B.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

**g) Probability of 1/4 inch grip given midsized head**

This is a conditional probability.

P(A | M) = P(A ∩ M) / P(M) = P(M,S) / [P(M,S) + P(M,M) + P(M,L)]

**h) Independence of events**

Events A and B are independent if P(A ∩ B) = P(A) * P(B).  Calculate P(A) * P(B) and compare it to the value you got for P(A ∩ B) in part (e).  If they are equal, the events are independent. If they are not equal, the events are dependent.

**Provide the table, and I'll calculate the specific probabilities for you!**