Question

name: eli santana
science course:
pre lab due:
post lab due:
grade: 9
background
probability lab
background
probability is the likelihood of a particular event happening. most people think of probability as a number between 0 and 1 (or 0% and 100%) expressing the chance that a particular thing will happen. while this may seem very practical, probability is actually a very abstract idea. for example, in biology, scientists that study genetics use probability to determine the chance that a particular trait will be passed on to offspring. in business, companies use probability to determine when to run sales or how to price items. probability is where consumers are more likely to look on the shelves or what products are more likely to be placed next to each other.
calculating probability
calculations

favorable / # total possible = %

observed / # total number of trials = %

examples
expected research: in a coin experiment if 1 of the 100 you test lands on heads, the probability is calculated by 1/100 = 1%
observed research: if the same experiment is 1 to be performed 10 times and the coin only landed on the 4 which isnt 1 once, 1/10 = 10%
prelab questions

1. when flipping a single coin, calculate the probability that it will land with the “heads” side up. show your work.
2. what is the probability that a single coin will land with the “tails” side up? show your work.

when flipping two coins at the same time, you have four different ways the coins can land: heads/heads, tails/tails, or heads/tails, or tails/heads.

1. when flipping two coins, calculate the probability that the coins will land with the both heads. show your work.
2. what is the probability that the 2 coins will land with both tails? show your work.
3. what is the probability that the 2 coins will land with the first coin heads up and the second coin tails up? show your work.
4. what is the probability that the 2 coins will land with the first coin tails up and the second heads? show your work.

three supplies are needed
procedure
for part 1
you will use a coin, paper, pencil/pen, and a clear cup. you can either flip the coin from the table or flip the coin in the cup and then flip the coin. record the results. you will flip the coin 10 times. make a tally mark for how many times it is heads or tails.
last: one coin flip data table
pips 1:10
pips 11:20
pips 21:30
pips 31:40
pips 41:50
pips 51:60
class totals

Explanation:

Problem 1: Probability of single coin landing on Heads

Step 1: Define possible outcomes

A fair coin has 2 possible outcomes: Heads (H) or Tails (T), so total outcomes \( n = 2 \), favorable outcomes for Heads \( f = 1 \).

Step 2: Apply probability formula

Probability \( P = \frac{\text{favorable outcomes}}{\text{total outcomes}}=\frac{1}{2}= 0.5 = 50\% \).

Step 1: Define outcomes

Total outcomes \( n = 2 \), favorable for Tails \( f = 1 \).

Step 2: Calculate probability

\( P=\frac{1}{2}= 0.5 = 50\% \).

Step 1: List all outcomes

Two coins: outcomes are (H,H), (H,T), (T,H), (T,T) → total \( n = 4 \). Favorable (both H) \( f = 1 \).

Step 2: Compute probability

\( P=\frac{1}{4}= 0.25 = 25\% \).

Answer:

\( \frac{1}{2} \) (or 50%)

Problem 2: Probability of single coin landing on Tails