Fill in the blanks.
(i) In a single throw of a dice, the probability of getting a number greater than 2 is `ul(P)`.
(ii) A card is drawn from a deck of 52 cards. The probability of drawing a red card is `ul(Q)` and a face card is `ul(R)`.
(iii) A bag contains 2 blue and 3 green marbles, then the probability of drawing a red marble `ul(S)`.

Options

A. `{:(P,Q,R,S),((1)/(3),(11)/(26),(2)/(11),1):}`
B. `{:(P,Q,R,S),((1)/(6),(1)/(4),(3)/(11),0):}`
C. `{:(P,Q,R,S),((2)/(3),(1)/(2),(3)/(13),0):}`
D. `{:(P,Q,R,S),((2)/(3),(1)/(2),(3)/(13),(3)/(5)):}`

Answer

Let's solve the question step by step.

### Step 1: Calculate the probability of getting a number greater than 2 when throwing a dice.

1. **Total Outcomes**: When throwing a single die, the possible outcomes are {1, 2, 3, 4, 5, 6}. Therefore, the total number of outcomes is 6.

2. **Favorable Outcomes**: We need to find the numbers greater than 2. The numbers greater than 2 are {3, 4, 5, 6}. Thus, the favorable outcomes are 4.

3. **Probability Calculation**: The probability \( P \) of getting a number greater than 2 is given by the formula:
\[ P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{4}{6} = \frac{2}{3} \]

### Step 2: Calculate the probability of drawing a red card from a deck of 52 cards.

1. **Total Outcomes**: The total number of cards in a standard deck is 52.

2. **Favorable Outcomes**: In a deck, there are 26 red cards (13 hearts and 13 diamonds).

3. **Probability Calculation**: The probability \( Q \) of drawing a red card is:
\[ Q = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{26}{52} = \frac{1}{2} \]

### Step 3: Calculate the probability of drawing a face card.

1. **Total Face Cards**: In a deck of cards, there are 12 face cards (3 face cards in each of the 4 suits).

2. **Probability Calculation**: The probability \( R \) of drawing a face card is:
\[ R = \frac{\text{Total Face Cards}}{\text{Total Outcomes}} = \frac{12}{52} = \frac{3}{13} \]

### Step 4: Calculate the probability of drawing a red marble from a bag containing blue and green marbles.

1. **Total Marbles**: The bag contains 2 blue and 3 green marbles, making a total of:
\[ 2 + 3 = 5 \text{ marbles} \]

2. **Favorable Outcomes**: There are no red marbles in the bag.

3. **Probability Calculation**: The probability \( S \) of drawing a red marble is:
\[ S = \frac{0}{5} = 0 \]

### Final Answers:
- (i) \( P = \frac{2}{3} \)
- (ii) \( Q = \frac{1}{2} \) and \( R = \frac{3}{13} \)
- (iii) \( S = 0 \)

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