Help please.

[TalaAZ]

A merchant imported sugar stews in two ships. If the probability of the first ship arriving on time is 60%, the probability of the second ship arriving on time is 50%, and the probability of both arriving together is 30%, then what is the probability of at least one of the two ships arriving on time?
Actually, my 10th grade sister asked me about this and I remember nothing of probability, so I would like to kindly ask for a simple and sufficient explanation.

 

[lex]

Perhaps find the probability of both ships not arriving on time and then take this answer from 1.

 

[Dr.Peterson]

Perhaps find the probability of both ships not arriving on time and then take this answer from 1.

Should "both arriving together" be "both arriving on time"? The former would include other cases, so the problem couldn't be solved.

The data allow two methods of solution, as you can show that the events are independent and use lex's method, or use the formula for P(A or B), which doesn't require independence.

 

[lex]

Should "both arriving together" be "both arriving on time"? The former would include other cases, so the problem couldn't be solved.

The data allow two methods of solution, as you can show that the events are independent and use lex's method, or use the formula for P(A or B), which doesn't require independence.

I didn't even notice!
Yes, if it really is both arriving together, then assuming they have the same deadline, that will give a different answer (based on [MATH]P(A\cap B)+P(\overline{A}\cap \overline{B})=0.3[/MATH])
(A ship 1 on time, B ship 2 on time)

 

[Dr.Peterson]

I didn't even notice!
Yes, if it really is both arriving together, then assuming they have the same deadline, that will give a different answer (based on [MATH]P(A\cap B)+P(\overline{A}\cap \overline{B})=0.3[/MATH])
(A ship 1 on time, B ship 2 on time)

Except that they can both be not on time without arriving together! What if one is early and the other late? That's not part of the 30%.

I'm hoping it was stated incorrectly.

 

[lex]

Of course, how silly; assuming the same deadline, [MATH]P(A\cap B)+P(\overline{A}\cap \overline{B})≥0.3[/MATH], not necessarily equal, as both together is only a subset of both early or both late. We could only give a range of values (between 0.6 and 0.9) for the answer, not a single value. We must assume it was a slip of the 'pen' then.