One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
(i)E : the card drawn is a spade F : the card drawn is an ace
(ii) E : the card drawn is black F : the card drawn is a king
(iii)E : the card drawn is a king or queen F : the card drawn is a queen or jack.

Explanation

To determine whether the events E and F are independent for each of the given cases, we need to check if the condition \( P(E \cap F) = P(E) \times P(F) \) holds true. Let's go through each case step by step.

### Case (i)
**Events:**
- E: The card drawn is a spade.
- F: The card drawn is an ace.

**Step 1: Calculate \( P(E) \)**
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