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You randomly select a coin from a jar containing 30 coins: 8 pennies, 10 nickels, 7 dimes, and 5 quarters.

What is the probability of:

selecting a penny?

selecting a nickel?

not selecting a dime?

selecting a dime or a quarter?

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The probability of selecting a penny is 4/15

The probability of selecting a nickel is 1/3

The probability of selecting a dime is 7/30

The probability of selecting a dime or a quarter is 2/5

Probability

From the formula for probability,

$$P(A) = \frac{Number\ of\ favourable\ outcomes\ to\ A}{Total\ number\ of\ possible\ outcomes}$$

Total number of possible outcomes = 30

- The probability of selecting a penny

$$P(penny) = \frac{8}{30}$$

$$P(penny) = \frac{4}{15}$$

The probability of selecting a penny is 4/15

- The probability of selecting a nickel

$$P(nickel) = \frac{10}{30}$$

$$P(nickel) = \frac{1}{3}$$

The probability of selecting a nickel is 1/3

- The probability of selecting a dime

$$P(dime) = \frac{7}{30}$$

The probability of selecting a dime is 7/30

- The probability of selecting a dime or a quarter

First, we will calculate the probability of selecting a quarter

$$P(quarter) = \frac{5}{30}$$

$$P(quarter) = \frac{1}{6}$$

Then, the probability of selecting a dime or a quarter is

$$P(dime \ or \ quarter) = \frac{7}{30}+ \frac{1}{6}$$

$$P(dime \ or \ quarter) = \frac{7+5}{30}$$

$$P(dime \ or \ quarter) = \frac{12}{30}$$

$$P(dime \ or \ quarter) = \frac{2}{5}$$

The probability of selecting a dime or a quarter is 2/5

Hence,

The probability of selecting a penny is 4/15

The probability of selecting a nickel is 1/3

The probability of selecting a dime is 7/30

The probability of selecting a dime or a quarter is 2/5