Just substitute 1 as the value and you will get your answer
Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2.
H - head
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T) = 0.8
urn
3 red and 5 blue
when heads is obtained
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12
when tails is obtained
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3
using bayes rule the answer can be found out,
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
= 0.12 / (0.12 + 0.3)
= 0.12 / 0.42
= 0.286
the final answer is 0.286
The number is 2/9 hope that helps!
