Binomial distrubution question

can someone help me figure out this binomial distribution question

Jasper has 3 coins.
In an experiment, Jasper flips each of the 3 coins and records the total number of heads that he gets.
Jasper believes that each coin is biased so that the number of heads he gets can be modelled by the binomial distribution, B(3,0.4)

(a) show that P(0 heads) = 0.216

the mark scheme says 0.6 to the power of 3 but i don't understand where 0.6 comes from and why it is to the power of 3

(b) work out the probability that the outcome of the experiment is exactly 1 head

this question im struggling on to any help?

Reply 1

username5086466

8

a) So 0.4 is the probability of landing on heads. Since we are trying to find P(0) it means we need the probability of all 3 coins landing on tails.
Since the probability is 0.4 for heads, this means the probability of tails is 0.6.

Because we are flipping the coin 3 times the probability of landing on tails 3 times will be 0.6 x 0.6 x 0.6 which is essentially 0.6 to the power of 3.

b) Using your calculator: Select binomial PD distribution (as we are trying to find the probability of a single result).
p= 0.4 (as probability of landing on head is 0.4)
n=3 (as 3 coins will be flipped)
x=1 (as we want to know the chance of only 1 head out of the 3 flips).

Hope this helps!

Reply 2

liamlarner

OP

13

Original post by dextrous63

Think it's a typo and they meant B(3,0.6). After that, p(X=3) is a straight use of the formula as is (b) ... p(X=1)

no the question is B(3,0.4)

Reply 3

T!gger34

15

Original post by liamlarner

no the question is B(3,0.4)

I'm having an off day. Sorry.

What would the formula for p(X=0) be?

Reply 4

the bear

20

for the binomial distribution ( 3, 0.4 ) the chance of getting n heads is ³C_n*(0.4)ⁿ*0.6^3-n

so for a) you let n = 0

b) you let n = 1

Reply 5

liamlarner

OP

13

Original post by Tom Woodrough

a) So 0.4 is the probability of landing on heads. Since we are trying to find P(0) it means we need the probability of all 3 coins landing on tails.
Since the probability is 0.4 for heads, this means the probability of tails is 0.6.

Because we are flipping the coin 3 times the probability of landing on tails 3 times will be 0.6 x 0.6 x 0.6 which is essentially 0.6 to the power of 3.

b) Using your calculator: Select binomial PD distribution (as we are trying to find the probability of a single result).
p= 0.4 (as probability of landing on head is 0.4)
n=3 (as 3 coins will be flipped)
x=1 (as we want to know the chance of only 1 head out of the 3 flips).

Hope this helps!

Thanks, ur a legend g