Question

Emma selects coins at random from a jar, putting the coin back each time after selecting it. She conducts 28 trials and selects 7 pennies, 12 nickels, and 9 dimes. Based on the results, describe in words the likelihood that she selects a penny?

Answer 1

Emma is most likely to select a penny in her trials, as she chose 7 pennies out of 28 total selections.

Step-by-step explanation:

In probability terms, the likelihood of an event happening is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability (P) of Emma selecting a penny can be expressed as the ratio of the number of pennies selected (7) to the total number of trials (28). Mathematically, this can be represented as:

`\[ P(\text{Selecting a Penny}) = (7)/(28) \]`

Simplifying this fraction, we get
`\( P(\text{Selecting a Penny}) = (1)/(4) \).`

Therefore, there is a 1 in 4 chance that Emma will select a penny in any given trial. This can also be expressed as a percentage by multiplying the probability by 100:

`\[ P(\text{Selecting a Penny}) = (1)/(4) * 100\% = 25\% \]`

So, based on the results of Emma's 28 trials, the probability or likelihood of her selecting a penny is 25%. The fact that she replaces the coin each time ensures that each trial is independent, and the probability remains consistent across all trials.