Stats Word Problem: probability of 0.4 that your ticket will be checked

Idonotknowmath

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On a single train journey there is a probability of 0.4 that your ticket will be checked. You make a return-journey, what is the probability that your ticket will be checked only once?
Give your answer as a proportion, rounding to two decimal places.







Can someone explain how to get the answer here? And why is it NOT .20? Unless it is … in which case great. But it can't be that easy …
 
On a single train journey there is a probability of 0.4 that your ticket will be checked. You make a return-journey, what is the probability that your ticket will be checked only once?
Give your answer as a proportion, rounding to two decimal places.

Can someone explain how to get the answer here? And why is it NOT .20? Unless it is … in which case great. But it can't be that easy …

Two possibilities:

You get checked going up but not going back and

You don't get checked going up but get checked going back.

Probability of getting checked both ways = 0.4*0.4 =0.16

Probability of not getting checked both ways = 0.6*0.6 =0.36

Continue....
 
0.48! I got it …

Ty. But I had to use the tree diagram to figure it out. Is there any other way? Without the tree diagram, I was lost. Also: Your breakdown of the problem from 0.6 (not getting checked) and 0.4 (getting checked) really helped me. But why couldn't I figure that out myself. It seemed really easy after you did it, so why couldn't I do it? Any advice there? Ty.
 
On a single train journey there is a probability of 0.4 that your ticket will be checked. You make a return-journey, what is the probability that your ticket will be checked only once?







Can someone explain how to get the answer here?
Where is "here"? Was there supposed to be text or an image in that big gap? Thank you! ;)
 
...But why couldn't I figure that out myself. It seemed really easy after you did it, so why couldn't I do it? Any advice there? Ty.
What you think was difficult 'yesterday' but seems easy 'today' is generally about having run into (and solved) a problem like it. Did you find the .4*.6*2 [or maybe .4*.6 + .4*.6] difficult? Would you even have know what that meant some x years ago?

That phenomena is one of the reasons why, when someone asks (about math, piano, ...) 'How can I learn this', the answer is generally 'Practice, Practice, Practice'
 
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