A coin is tossed and a die is thrown what is the probability of getting a head and a perfect square
To solve this problem, we need to determine the probability of getting a head on a coin toss and a perfect square on a die throw individually, and then multiply the two probabilities together.
1. Probability of getting a head on a coin toss:
Since the coin has two equally likely outcomes (head or tail), the probability of getting a head is 1/2.
2. Probability of getting a perfect square on a die throw:
A standard die has 6 faces, numbered from 1 to 6. The perfect squares on a die are 4 and 6. The probability of rolling a perfect square on a die throw is 2/6, which simplifies to 1/3.
Now, we multiply the probabilities together:
Probability of getting a head and a perfect square = Probability of getting a head × Probability of getting a perfect square = 1/2 × 1/3 = 1/6.
Therefore, the probability of getting a head and a perfect square is 1/6.
To find the probability of getting a head and a perfect square when a coin is tossed and a die is thrown, we need to consider the possible outcomes and count the favorable outcomes.
Let's first identify the possible outcomes for each event:
Coin toss: There are two possible outcomes, either a head or a tail.
Die throw: There are six possible outcomes, corresponding to the numbers 1, 2, 3, 4, 5, and 6 on the sides of the die.
To find the favorable outcomes that satisfy both conditions (head and perfect square), we need the coin to land on heads (1 outcome) and the die to show a perfect square (2 outcomes: 4 or 6). So there are 1 x 2 = 2 favorable outcomes.
Since we know there are 2 possible outcomes for the coin toss and 6 possible outcomes for the die throw, the total number of outcomes is 2 x 6 = 12.
The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
= 2 / 12
= 1 / 6
≈ 0.1667
Therefore, the probability of getting a head and a perfect square is approximately 0.1667 or 1/6.
To find the probability of getting a head and a perfect square when flipping a coin and throwing a die, you need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Number of favorable outcomes:
- Getting a head and a perfect square.
- Heads can only occur once, and perfect squares on a die are 4 and 9.
So, there is only one favorable outcome.
2. Total number of possible outcomes:
- When flipping a coin, there are 2 possible outcomes (heads or tails).
- When throwing a die, there are 6 possible outcomes (numbers from 1 to 6).
Multiplying the number of possibilities for each event, we find that the total number of possible outcomes is 2 * 6 = 12.
3. Calculating the probability:
- Probability = Number of favorable outcomes / Total number of possible outcomes
- Probability = 1 / 12
So, the probability of getting a head and a perfect square is 1/12.