Question

Peter calculated that the theoretical probability of obtaining exactly two heads when flipping six coins is 23.4%. What number of heads also has a 23.4% theoretical probability of coming up when 6 coins are flipped?

Answer 1

Answer:

The theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.

Step-by-step explanation:

Getting x successes out of n trials is a binomial distribution and is given by:

p(x) = $nC_{x} p^{n-x} q^{x}$

Here, n = 6

x = 2

p = probability of one head = $\frac{1}{2}$

q = 1 - p

= $1-\frac{1}{2}$

= $\frac{1}{2}$

Substitute these values, we get,

p(2) = $6C_{2} (\frac{1}{2} )^{6-2} (\frac{1}{2} )^{2}$

= $15(\frac{1}{2} )^{6}$

= $\frac{15}{64}$

= 0.234

= 23.4%

We know that $6C_{2} =6C_{6-2}$

$6C_{2} =6C_{4}$

Now,

p(4) = $6C_{4} (\frac{1}{2} )^{6-4} (\frac{1}{2} )^{4}$

= $15(\frac{1}{2} )^{6}$

= p(2)

Hence, the theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.