Two probability questions. Even HOW to do it would be a huge help

#1
1.Mary has two friends, Ann and Sarah. Mary will visit Ann this evening if the 19A bus arrives before 6PM. Otherwise, She will visit Sarah. The probability of the 19A bus arriving before 6pm is 40%. If she visits Ann, the probability that Ann will be at home is 10% and if she visits Sarah, the probability that Sarah will be home is 20%. Find the probability that the friend Mary visits will be home

2.A darts player finds that on average he hits the bullseye 4 times out of 5. Calculate the probability that in a random sample of 4 shots, he will miss the bullseye at least 3 times
 
#3
Do you know the law of total probability?

Do you know if the binomial distribution?
I know the general binomial distribution and applied in to the darts question but didn't get the right answer. Can you expand on the law of total probability please?
 

Dason

Ambassador to the humans
#4
Can you show what you did for the second question, the answer you got, and what you think the correct answer is?
 
#5
Can you show what you did for the second question, the answer you got, and what you think the correct answer is?
n= no of trials=4
p=probability of success=0.2
q=probability of failure=0.8
x=no of successes in n trials=3 or 4
P(x<=4, but>=3)=P(x=4)+P(x=3)
=(4C4 x (0.2)^4 x (0.8)^0)+(4C3 x (0.2)^3 x (0.8)^1))
=(0.1667x0.0016x1)+(2x0.008x0.8)
=0.013

The correct answer is 0.0272
 

Dason

Ambassador to the humans
#6
All of your work for that is correct except for one thing. In both cases where your calculating using the "choose" function you're getting it wrong.

4C4 is 1 and 4C3 is 4. I'm not sure how you're getting your answers of 1/6 and 2 but that seems to be your issue with that problem.
 
#7
All of your work for that is correct except for one thing. In both cases where your calculating using the "choose" function you're getting it wrong.

4C4 is 1 and 4C3 is 4. I'm not sure how you're getting your answers of 1/6 and 2 but that seems to be your issue with that problem.
Brilliant, thank you so much for your help!