A coin is tossed 8 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.
P(4 heads)=we want 4 of 8 heads
8 nCr 4 (1/2)^4(1-1/2)^8-4
70(1/16)*(1/2)^4
I am lost from here
I don't understand why you stopped in the middle of your arithmetic,
after all you just found (1/2)^4 = 1/16
What was different in the (1/2)^4 further along your answer ??
8C4 (1/2)^4(1-1/2)^8-4
= 70(1/16)(1/16) = 70/256
= 35/128
To find the probability of getting exactly 4 heads when a coin is tossed 8 times with a probability of 0.5 for each head, we can use the binomial probability formula.
The formula for the probability of getting exactly k successes (heads) in n independent trials is:
P(k) = n C k * p^k * q^(n-k)
Where:
- n C k means "n choose k," which represents the number of combinations of n items taken k at a time.
- p is the probability of success (in this case, the probability of getting a head on any one toss).
- q is the probability of failure (in this case, the probability of getting a tail on any one toss), which is equal to 1 - p.
Now, let's calculate the probability of getting exactly 4 heads:
P(4) = 8 C 4 * (0.5)^4 * (1 - 0.5)^(8 - 4)
To calculate 8 C 4 (8 choose 4), we can use the formula:
n C k = n! / (k! * (n - k)!)
8 C 4 = 8! / (4! * (8 - 4)!)
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
Calculating the above expression:
8 C 4 = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (4 * 3 * 2 * 1)]
= (8 * 7 * 6 * 5) / (4 * 3 * 2)
= 70
Therefore, P(4) = 70 * (0.5)^4 * (0.5)^(8 - 4).
Calculating further:
P(4) = 70 * (0.5)^4 * (0.5)^4
= 70 * (1/16) * (1/16)
= 70/256
≈ 0.273
The probability of getting exactly 4 heads when tossing a coin 8 times with a probability of 0.5 for each head is approximately 0.273, to the nearest thousandth.