Respuesta :
Answer:
Step-by-step explanation:
Out of the 7 coins, one is fake and has heads on both sides. So, fake coin on toss coin will always turns up to be head.
Therefore, to obtain the probability of exactly 5 heads is:
probability of getting exactly 4 heads from the 6 fair coins
Probability of getting heads, p = [tex]\frac{1}{2} [/tex]
Probability of not getting head, q = 1 - p = [tex]\frac{1}{2} [/tex]
Now, by Binomial distribution with:
p = [tex]\frac{1}{2} [/tex] = 0.5
q = [tex]\frac{1}{2} [/tex] = 0.5
n = 6
P(X = r) = [tex]^{n}C_{r} p^{r} q^{n - r}[/tex]
P(X = 4) = [tex]^{6}C_{4} p^{4} q^{2}[/tex]
P(X = 4) = [tex]^{6}C_{4} \times 0.5^{4}\times 0.5^{2}[/tex]
P(X = 4) = [tex]\frac{6!}{4!(6 - 4)!} \times 0.5^{4}\times 0.5^{2}[/tex]
On solving the above eqn, we get:
P(X = 4) = 0.2344
Therefore, the probability of getting exactly 5 heads is 0.2344
We will see that the probability of obtaining exactly 5 heads is:
P = 0.164
How to find the probability?
The probability of getting tails in one toss is 0.5, and the probability of getting heads in one toss is 0.5
Then, if out of 7 tosses we have 5 heads and 2 tails, the probability is:
P = (0.5)^2*(0.5)^5
And we also need to find the possible permutations, this is, the number of different groups of 5 that we can make with the 7 coins, this is given by:
[tex]C(7, 5) = \frac{7!}{(7 - 5)!*5!} = \frac{7*6}{2} = 21[/tex]
So the total probability will be:
P = 21*(0.5)^2*(0.5)^5 = 0.164
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
