Probability of Obtaining Exactly 2 Heads when Tossing 6 Coins

To calculate the probability of obtaining exactly 2 heads when tossing 6 coins simultaneously, we need to use the concept of combinations and the probability of getting a head or a tail on a single coin toss.

Step 1: Determine the Sample Space
The sample space refers to all possible outcomes of an experiment. In this case, when tossing 6 coins simultaneously, each coin can either land on heads (H) or tails (T). Therefore, the sample space consists of all possible combinations of H and T for 6 coins, which is 2^6 = 64.

Step 2: Determine the Number of Favorable Outcomes
The favorable outcomes are those that meet the condition of obtaining exactly 2 heads. To calculate this, we need to determine the number of ways we can select 2 positions out of the 6 available positions for the heads. This can be calculated using the combination formula:

C(n, r) = n! / (r! * (n-r)!)

where n is the total number of items, and r is the number of items to be selected.

In this case, we have n = 6 (total number of positions) and r = 2 (number of positions for the heads). Therefore, the number of favorable outcomes is given by:

C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15

Step 3: Calculate the Probability
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes (sample space).

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

In this case, the probability of obtaining exactly 2 heads when tossing 6 coins is:

P(2H) = 15 / 64 = 0.2344

Therefore, the probability of obtaining exactly 2 heads when tossing 6 coins simultaneously is 0.2344 or 23.44%.

Visually Appealing Answer:
Probability of Obtaining Exactly 2 Heads when Tossing 6 Coins

Step 1: Determine the Sample Space
- Sample space consists of all possible combinations of H and T for 6 coins
- Total possible outcomes = 2^6 = 64

Step 2: Determine the Number of Favorable Outcomes
- Number of ways to select 2 positions out of 6 for the heads
- Using combination formula: C(6, 2) = 6! / (2! * (6-2)!) = 15

Step 3: Calculate the Probability
- Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
- Probability = 15 / 64 = 0.2344 or 23.44%