Three coins are tossed simultaneously ,find the probability of getting at least2 heads
There are 2 possible outcomes for each coin toss (heads or tails). Therefore, there are 2 × 2 × 2 = 8 possible outcomes when three coins are tossed simultaneously.
To find the probability of getting at least 2 heads, we need to calculate the probability of getting exactly 2 heads and the probability of getting all 3 heads, and then add these probabilities together.
Probability of getting exactly 2 heads:
There are three ways to get exactly 2 heads: HHT, HTH, and THH (where H represents heads and T represents tails). Each of these outcomes has a probability of (1/2) × (1/2) × (1/2) = 1/8. Therefore, the probability of getting exactly 2 heads is 3/8.
Probability of getting all 3 heads:
There is only one way to get all 3 heads: HHH. The probability of this outcome is (1/2) × (1/2) × (1/2) = 1/8.
Therefore, the probability of getting at least 2 heads is 3/8 + 1/8 = 4/8 = 1/2.
So, the probability of getting at least 2 heads when three coins are tossed simultaneously is 1/2 or 50%.
Find the depth of a pond if its radius is 1.5m and the amount of water it can hold is 755.6 liters.
The volume of a pond is given by the formula: V = πr^2h, where r is the radius of the pond and h is the depth of the pond.
We are given that the radius of the pond is 1.5m and the amount of water it can hold is 755.6 liters. We need to find the depth of the pond.
We know that 1 liter of water is equal to 0.001 cubic meters. Therefore, the volume of water the pond can hold in cubic meters is:
755.6 liters x 0.001 m^3/liter = 0.7556 m^3
Using the formula for the volume of a pond, we have:
V = πr^2h
0.7556 m^3 = π(1.5m)^2h
0.7556 m^3 = 7.0686 m^2h
h = 0.7556 m^3 / 7.0686 m^2
h = 0.107 m or 10.7 cm
Therefore, the depth of the pond is approximately 10.7 cm when its radius is 1.5m and the amount of water it can hold is 755.6 liters.
To find the probability of getting at least 2 heads when three coins are tossed simultaneously, we can use the concept of counting favorable outcomes and total outcomes.
Step 1: Determine the total number of possible outcomes when three coins are tossed simultaneously. Since each coin has two possible outcomes (either heads or tails), the total number of outcomes is 2 * 2 * 2 = 8.
Step 2: Determine the number of favorable outcomes that result in at least 2 heads. We have the following possibilities:
- HHT: This represents getting two heads and one tail.
- HTH: This also represents getting two heads and one tail.
- THH: This represents getting two heads and one tail.
- HHH: This represents getting all three heads.
There are a total of 4 favorable outcomes.
Step 3: Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 8
Probability = 0.5
Therefore, the probability of getting at least 2 heads when three coins are tossed simultaneously is 0.5 or 50%.