Agroup of 120 people touring europe includes 45 people who speak french, 42 who speak spanish, and 50 who speak neither language. what is the probability that a randomly chosen tourist from this group will speak both french and spanish?

Answer :

Explanation:

Since we have given that

n(U) = 120, where U denotes universal set ,

n(F) = 45, where F denotes who speak French,

n(S) = 42 , where S denotes who speak Spanish,

n(F∪S)' = 50

n(F∪S) = n(U)-n(F∪S) = 120-50 = 70

Now, we know the formula, i.e.

n(F∪s) = n(F)+n(S)-n(F∩S)

⇒  70    = 45+42-n(F∩S)

⇒ 70  =  87- n(F∩S)

⇒ 70-87 = -n(F∩S)

⇒ -17 = -n( F∩S)

⇒  17 = n(F∩S)

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