Question

Jay was reaching into her purse and accidentally spilled her coin purse. 10 pennies fell on the floor. Jay noticed that only 2 of the pennies landed on heads. What is the theoretical probability of this happening?

Answer 1

The theoretical probability of landing on 2 heads, when 10 coins are tossed is 0.0439 or 4.39%.

Explanation:

Number of coins that fell on the floor = 10

Number of coins that landed on heads = 2

We have to find the theoretical probability of getting 2 coins landing of heads when 10 coins are tossed.

Notice that there are only 2 possible outcomes: Either that coin will land on head or it won't. Landing of each coin is independent of the others coins. Probability of each coin landing on head is constant i.e. 0.5 or 1/2. Number of trials, i.e. the number of times the experiment will be done is fixed, which is 10.

All the 4 conditions for an experiment to be considered a Binomial Experiment are satisfied. So we will use Binomial Probability to solve this problem.

Probability of success = Probability of coin landing on head = 0.5

Number of trials = n = 10

Number of success = r = 2

The formula for Binomial Probability is:

`P(X = x) =^(n)C_(r)(p)^(r)(1-p)^(n-r)`

Using the values, we get:

`P(X=2)=^(10)C_(2)(0.5)^2(0.5)^8=0.0439`

Thus, the theoretical probability of landing on 2 heads, when 10 coins are tossed is 0.0439 or 4.39%.