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THE MODAL VERBS OF PROBABILITY

We can use these modal verbs (also called modals of deduction, speculation or certainty) when we want to make a guess about something. We choose the verb depending on how sure we are.
1: Talking about the present:
must / might / could / may / can't + infinitive

For example:
-I am waiting for Julie with another friend, David.

-I ask: 'Where is Julie?'
-David guesses:
+She must be on the bus. (I'm fairly sure this is a good guess)
+She might come soon. (maybe)
+She could be lost. (maybe)
+She may be in the wrong room. (maybe)
+She can't be at home. (I'm fairly sure this isn't true)
Notice that the opposite of 'must' is 'can't in this case.
Will / Won't:
We use will and won't when we are very sure:
-She'll be at work now.
Should / Shouldn't:
Should and shouldn't are used to make an assumption about what is probably true, if everything is as we expect:
-They should be there by now.
-It shouldn't take long to drive here.
This use of should isn't usually used for negative events. Instead, it's a better idea to use will:
-The underground will be very busy now (not: 'should be').
Can:
Can is used for something that is generally possible, something we know sometimes happens:
-Prices can be high in London.
Can is not used to talk about specific possibilities:
-He could be on the bus (not: 'can be').
2: Using modal verbs to talk about the past:
must / might / could / may / can't + have + past participle
+ must have + past participle
+ might / might not have + past participle
+ could / couldn't have + past participle
+ may / may not have + past participle
+ can't have + past participle
For example:
-You ask: Where was Julie last night?

-David answer:
+She must have forgotten about our date.
+She might have worked late.
+She could have taken the wrong bus.
+She may have felt ill.
+She can't have stayed at home.
+ Will / won't + have + past participle
Will and won't / will not + have + past participle are used for past certainty (compare with present use of 'will' above):
-The parcel will have arrived before now.
+ Should + have + past participle
Should + have + past participle can be used to make an assumption about something that has probably happened, if everything is as we expect (compare with present use of 'should' above):
-The train should have left by now.
Could:
We can use could + infinitive to talk about a general possibility in the past (compare with the use of 'can' above):
-Prices could be high in the sixteenth century.
This is not used to talk about specific possibilities in the past (instead we use could + have + past participle):
He could have been working late (not: 'could be'. As this is a specific possibility, 'could be' is present tense).

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