Four coins are tossed. What is the probability of getting more tails than heads and getting at least two heads?
The sample space consists of 24=16 outcomes.
A. more tails than heads:
1. exactly three tails:
TTTH TTHT THTT HTTT
2. exactly four tails:
TTTT
So calculate the probability.
You can try in a similar way to solve the second part.
To find the probability of getting more tails than heads and getting at least two heads when four coins are tossed, we can use the concept of counting favorable outcomes over the total number of possible outcomes.
Step 1: Count the favorable outcomes:
In this case, we want to get more tails than heads and at least two heads. Let's break it down into cases:
Case 1: Three tails and one head:
The possible outcomes for this case are TTHH, THTH, and THTT. So, there are three favorable outcomes in this case.
Case 2: Four tails:
The only possible outcome for this case is TTTT, which is one favorable outcome.
Hence, we have a total of four favorable outcomes.
Step 2: Count the total number of possible outcomes:
When tossing four coins, each coin has two possible outcomes (heads or tails). Therefore, the total number of possible outcomes is 2^4, which is 16.
Step 3: Calculate the probability:
The probability is calculated by dividing the favorable outcomes by the total number of possible outcomes. In this case, the probability is 4 favorable outcomes divided by 16 total outcomes, which simplifies to 1/4 or 0.25.
Therefore, the probability of getting more tails than heads and getting at least two heads when four coins are tossed is 0.25 or 1/4.