The probability of rolling a 6 on a biased dice is 1/5.

b) work out the probability of rolling exactly one six.

The question is on tree diagrams.

Step-by-step explanation:

The probability of rolling exactly one 6 depends on how many times the dice is rolled. Using binomial probability:

P = nCr p^r q^ (n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

Here, r = 1 and p = 1/5.

P = nC₁ (1/5) ¹ (4/5) ⁿ⁻¹

P = n (1/5) (4/5) ⁿ⁻¹

If the dice is rolled one time, the probability of exactly one 6 is:

P = 1 (1/5) (4/5) ¹⁻¹

P = 1/5

If the dice is rolled two times, the probability of exactly one 6 is:

P = 2 (1/5) (4/5) ²⁻¹

P = 8/25

So on and so forth.