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Statistics
EXERCISE 14.1
CBSE_NCERT_TEXTBOOK
Grade 10
Question:
A piggy bank contains hundred 50p coins, fifty ` 1 coins, twenty ` 2 coins and ten ` 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 ` 5 coin?
Step-by-Step Solution
Key Concept: Probability of an event = (Number of favourable outcomes) ÷ (Total number of equally likely outcomes).
1. Count the total number of coins\ \[\text{Total coins}=100+50+20+10=180\]\ 2. (i) Probability of getting a 50p coin\ - Favourable outcomes = number of 50p coins = 100.\ - Hence, \[P(\text{50p coin}) = \frac{100}{180}=\frac{10}{18}=\frac{5}{9}.\]\ 3. (ii) Probability that the coin is NOT a \`5 coin\ - Coins that are not \`5 = total coins – \`5 coins = 180 – 10 = 170.\ - Hence, \[P(\text{not \`5 coin}) = \frac{170}{180}=\frac{17}{18}.\]