Question

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Answer 1

Question :

A and B are events such that P ( A ) = 0.42, P ( B ) = 0.48 and P ( A and B ) = 0.16 determine

1. P ( not A )
2. P ( A or B )

Solution :

Determine P ( not A )

Probability of an event 'A' P ( A ) = 0.42

Complement of event 'A' is 'not A'

Probability of an event not A = P ( not A )

We know

P( A ) + P ( not A ) = 1

⇒ 0.42 + P ( not A ) = 1

⇒ P ( not A ) = 1 - 0.42

⇒ P ( not A ) = 0.58

Therefore the probability of an event 'not A' is 0.58

Determine P ( A and B )

Probability of an event 'A' P ( A ) = 0.42 = 42 / 100 = No. of favourable outcomes / No. of possible outcomes

⇒ No. of favaourable outcomes of event 'A' n( A ) = 42

⇒ No. of possible outcomes = 100

Probability of event 'B' P ( B ) = 0.48 = 48 / 100 = No. of favourable outcomes / No. of possible outcomes

⇒ No. of favourable outcomes of event 'B' n( B ) = 48

Probability of an event 'A and B' P ( A and B ) = 0.16 = 16 / 100 = No. of favourable outcomes / No. of possible outcomes

⇒ No. of favourable outcomes of even 'A and B' n( A ⋂ B ) = 16

Using relation

⇒ n( A ⋃ B ) = n( A ) + n( B ) - n( A ⋂ B )

= 42 + 48 - 16

= 90 - 16

= 74

Let the event be 'A or B'

No. of favourable outcomes n( A ⋃ B ) = 74

Probability of event 'A or B' P ( A or B ) = No. of favourable outcomes / No. of possible outcomes = 74 / 100 = 0.74

Therefore the probability of event 'A or B' is 0.74

Answer 2

Answer:

hope u understand friend.....