Question

When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?

Answer 1

The probability of getting exactly 3 heads in 6 flips of a fair coin is calculated using the binomial probability formula and is found to be 31.25%.

Step-by-step explanation:

The student is asking about the probability of getting a specific number of heads when flipping a coin multiple times. Since the probability of getting heads on a single flip is 0.5, and the coin tosses are independent events, we can use the binomial probability formula to calculate this. For exactly 3 heads out of 6 flips, the formula is given by: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful events we are looking for, p is the probability of success on a single trial, and C(n, k) is the combination of n items taken k at a time.

To find the probability of getting exactly 3 heads out of 6 flips, we plug in the values: n=6, k=3, and p=0.5:

P(X=3) = C(6, 3) * (0.5)^3 * (0.5)^(6-3) = 20 * (0.5)^3 * (0.5)^3

Calculating the combination C(6, 3) gives us 20, and raising 0.5 to the power of 3 gives us 0.125. Multiplying these together, we get:

P(X=3) = 20 * (0.125) * (0.125) = 20 * 0.015625 = 0.3125

So the probability of getting exactly 3 heads in 6 flips of a fair coin is 0.3125 or 31.25%.

Answer 2

The probability of getting exactly 3 head=0.3125

Step-by-step explanation:

Given that probability of getting head p=0.5

So probability of getting tail q=0.5

Number of coin toss n=6

And number of trial r=3

We know that from Binomial distribution function,the probability given as follows

`P=_(r)^(n){p^rq^(n-r)}`

So now by putting the values

`P=_(3)^(6)* {0.5^3* 0.5^(6-3)}`

Now by solving this

The probability of getting exactly 3 head=0.3125