Question

If you flip a fair coin 6 times,what is the probability that you will get exactly 4 tails

Answer 1

The probability of getting exactly 4 tails when flipping a fair coin 6 times is 0.234375, or about 23.44%.

Step-by-step explanation:

To find the probability of getting exactly 4 tails when flipping a fair coin 6 times, we can use the binomial probability formula. The formula is:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

• P(X=k) is the probability of getting k tails (in this case, k=4)
• n is the number of trials (in this case, n=6)
• p is the probability of getting a tail on a single trial (in this case, p=0.5)
• C(n, k) is the number of combinations of n things taken k at a time (in this case, C(6, 4) = 15)

Plugging these values into the formula, we get:

P(X=4) = 15 * 0.5^4 * (1-0.5)^(6-4) = 15 * 0.0625 * 0.25 = 0.234375

So, the probability of getting exactly 4 tails when flipping a fair coin 6 times is 0.234375, or about 23.44%.

Answer 2

0.234

Step-by-step explanation:

Given : You flip a fair coin 6 times

To Find: What is the probability that you will get exactly 4 tails

Solution:

Formula :
`P(X=r) =^nC_r p^r q^(n-r)`

Where r is the no. of success

n is the total no. of trials

p is the probability of success

q is the probability of failure

In This case success is getting tail

So, Probability of getting tail =
`(1)/(2)`

So, Probability of not getting tail =
`(1)/(2)`

n = 6

r = 4

`p =(1)/(2)`

`q=(1)/(2)`

Substitute the values in the formula

`P(X=4) =^6C_4 ((1)/(2))^4 ((1)/(2))^(6-4)`

`P(X=4) =(6!)/(4!(6-4)!)((1)/(2))^4 ((1)/(2))^(2)`

`P(X=4) =0.234`

Hence the probability that you will get exactly 4 tails is 0.234