A coin is tossed 10 times. The probability of getting a head on any one toss is
0.5. To the nearest thousandth, find the probability of getting 4 heads.
I got this my equation I need input it into a calculator
To find the probability of getting 4 heads when a coin is tossed 10 times, we can use the binomial probability formula.
The binomial probability formula is given by:
P(k) = (nCk) * p^k * (1 - p)^(n - k)
Where:
P(k) is the probability of getting exactly k successes,
n is the number of trials (in this case, the number of tosses),
p is the probability of success on a single trial (in this case, the probability of getting a head, which is 0.5),
k is the number of successes (in this case, 4).
Using the formula, we can calculate the probability step by step:
1. Calculate the binomial coefficient (nCk), which represents the number of ways to choose k successes out of n trials. The binomial coefficient (nCk) can be calculated using the formula:
(nCk) = n! / (k! * (n - k)!)
In this case, n = 10 and k = 4, so we have:
(10C4) = 10! / (4! * (10 - 4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
2. Calculate the probability of getting 4 heads (p^k). In this case, p = 0.5 and k = 4, so we have:
(0.5)^4 = 0.0625
3. Calculate the probability of getting 6 tails [(1 - p)^(n - k)]. In this case, p = 0.5, n = 10, and k = 4, so we have:
(1 - 0.5)^(10 - 4) = 0.5^6 = 0.015625
4. Multiply the above three values together to get the final probability:
P(4) = (10C4) * (0.5)^4 * (1 - 0.5)^(10 - 4) = 210 * 0.0625 * 0.015625 = 0.2041015625
So, rounding to the nearest thousandth, the probability of getting 4 heads when a coin is tossed 10 times is approximately 0.204.