MATH SOLVE

5 months ago

Q:
# Binomial distribution: find the probability that in 10 tosses of a coin you will get 3 to 6 heads

Accepted Solution

A:

When tossing a coin, you have 50% chance of landing a head.
Now, use the binomial formula to find the probability of landing 3 to 6 heads when a coin is tossed 10 times.
$$ P\left(X=x\right)=\left(_nC_x\right)\times p^x\times\left(1-p\right)^{n-x} $$
Where:
n = number of trials
x = number of successes at n trials
p = probability of success
As given,
n = 10, x = 3 to 6, p = 50% = 0.50
Therefore,
$$ P\left(3\le x\le6\right)=\sum_{x\mathop{=}3}^6\left(_{10}C_x\right)\times\left(0.50\right)^x\times\left(1-0.50\right)^{10-x}, $$
$$ P\left(3\le X\le6\right)=0.7734 $$