What is the probability that at least two heads are obtained when a coin is tossed 3 times?

To find the probability of getting at least two heads when a coin is tossed 3 times, we need to calculate the probability of getting exactly 2 heads and the probability of getting exactly 3 heads, and then add them together.

The probability of getting exactly 2 heads in 3 coin tosses can be calculated using the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:
- n is the number of trials (3 coin tosses)
- k is the number of successful outcomes (2 heads)
- p is the probability of success on a single trial (0.5 for a fair coin)

P(X=2) = (3 choose 2) * (0.5)^2 * (0.5)^(3-2)
P(X=2) = 3 * 0.25 * 0.5
P(X=2) = 0.375

The probability of getting exactly 3 heads in 3 coin tosses is:

P(X=3) = (3 choose 3) * (0.5)^3 * (1-0.5)^(3-3)
P(X=3) = 1 * 0.125 * 1
P(X=3) = 0.125

Therefore, the probability of getting at least two heads when a coin is tossed 3 times is:

P(at least 2 heads) = P(X=2) + P(X=3)
P(at least 2 heads) = 0.375 + 0.125
P(at least 2 heads) = 0.5

So, the probability of getting at least two heads when a coin is tossed 3 times is 0.5 or 50%.

The probability of getting at least two heads when a coin is tossed 3 times is 0.75.

Here is the breakdown of all possible outcomes:

HHH (all heads): 1/8
HHT (2 heads, 1 tail): 3/8
HTH (2 heads, 1 tail): 3/8
THH (2 heads, 1 tail): 3/8
HHTT (1 head, 2 tails): 3/8
HTTH (1 head, 2 tails): 3/8
THHT (1 head, 2 tails): 3/8
TTT (all tails): 1/8

As you can see from the breakdown, there are 7 out of 8 possible outcomes that result in at least two heads. Therefore, the probability of getting at least two heads is 7/8 = 0.75.