Unit 8 - m1 perform a calculation using probability to investigate a scientific problem

Unit 8 – using statistics in science
M1 - Perform a calculation using probability to investigate a scientific problem
A scientist growing two different microorganisms knows that the probability of growing type A is
0.3 and the probability of growing type B is 0.5 and P(AǀB) = 0.25. Find:

P(A|B)
Event A happening, given that event B has already happened

P( A ∩ B)
P( A∨B)=
P( B)

0.125
P( A∨B)=
0.5

P ( A|B )=0.25

P(A∩B)
Probability of both A and B both happening

P ( A ∩B )=P ( B ) × P( A∨B)

P ( A ∩B )=0.5 ×0.25

P ( A ∩B )=0.125

P(A∪B)
Probability of either A or B happening

P ( A ∪ B ) =P ( A )+ P ( B )−P ( A ∩ B )

P ( A ∪B ) =0.3+0.5−0.125

P ( A ∪ B ) =0.675

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