A piggy bank contains hundred 50p coins, fifty Rs. 1 coins, twenty ? 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a 50 p coin? (ii) will not be a Rs. 5 coin?

Options

A. `9/5" "1/6" "5/8" "11/18`
B. `7/18" "3/8" "5/7" "12/18`
C. `1/6" "7/18" "3/8" "13/18`
D. `5/9" "1/6" "17/18" "7/18`

Explanation

To solve the problem step by step, we will find the total number of coins in the piggy bank and then calculate the probabilities for the two parts of the question.

### Step 1: Calculate the total number of coins in the piggy bank.
- Number of 50p coins = 100
- Number of Rs. 1 coins = 50
- Number of Rs. 2 coins = 20
- Number of Rs. 5 coins = 10

**Total number of coins** = Number of 50p coins + Number of Rs. 1 coins + Number of Rs. 2 coins + Number of Rs. 5 coins
= 100 + 50 + 20 + 10
= 180

### Step 2: Calculate the probability that the coin will be a 50p coin.
- **Favorable outcomes** (number of 50p coins) = 100
- **Total outcomes** (total number of coins) = 180

**Probability of drawing a 50p coin** = (Number of favorable outcomes) / (Total number of outcomes)
= 100 / 180
= 10 / 18
= 5 / 9

### Step 3: Calculate the probability that the coin will not be a Rs. 5 coin.
- **Favorable outcomes** (number of coins that are not Rs. 5 coins) = Number of 50p coins + Number of Rs. 1 coins + Number of Rs. 2 coins
= 100 + 50 + 20
= 170

**Probability of not drawing a Rs. 5 coin** = (Number of favorable outcomes) / (Total number of outcomes)
= 170 / 180
= 17 / 18

### Final Answers:
(i) The probability that the coin will be a 50p coin is **5/9**.
(ii) The probability that the coin will not be a Rs. 5 coin is **17/18**.

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