Emory tosses a nickle four times. The probability that he gets at least as many heads as tails is? Explain

To find the probability that Emory gets at least as many heads as tails when tossing a nickel four times, we need to count the number of favorable outcomes and the total number of possible outcomes.

Let's break it down step by step:

Step 1: Determine the possible outcomes of a single coin toss
When tossing a coin, there are two possible outcomes: heads (H) or tails (T).

Step 2: Calculate the total number of outcomes for four coin tosses
Since each coin toss has two possible outcomes, we need to multiply these possibilities together for four tosses.
Total number of outcomes = 2 x 2 x 2 x 2 = 2^4 = 16

Step 3: Count the favorable outcomes where Emory gets at least as many heads as tails
To calculate the favorable outcomes, we need to consider the possible combinations of H and T for four tosses. We will start by counting the cases where Emory gets an equal number of heads and tails and then add the cases where he gets more heads than tails.

Option 1: Equal number of heads and tails (2 heads, 2 tails):
There are several ways to arrange 2 heads and 2 tails in four tosses, namely HH, HT, TH, or TT.

Option 2: More heads than tails (3 heads, 1 tail) or (4 heads, 0 tails):
We can have HHTT, HHTH, HTHH, or HHHH.

So, in total, there are 4 favorable outcomes.

Step 4: Calculate the probability
Now that we know the total number of outcomes is 16 and the favorable outcomes are 4, we can calculate the probability using the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)

Probability = 4 / 16 = 1/4 = 0.25

Therefore, the probability that Emory gets at least as many heads as tails when tossing a nickel four times is 0.25 or 25%.