P(B)= 9/20 P(A and B)= 9/100 P(A)=?

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Answer 1 · 2018-04-12T03:54:34

#P(A)=1/5#

Assuming events #A# and #B# are independent, we use

#"P"(A nn B) = "P"(A) * "P"(B)#

#"         "9/100 = "P"(A) * 9/20#

#20/9 * 9/100 = "P"(A)#

#"         "20/100="P"(A)#

#"             "1/5="P"(A)#

Answer 2 · 2018-04-30T18:15:36

#P(A) = 1/5#

#P (A and B) = P(A) * P(B)#

-

#P (B) = 9/20#

#P (A and B) = 9/100#

#P (A) = (P(A and B))/(P(B))#

#(P(A and B))/(P(B)) = 9/100 div 9/20#

#= 9/100 * 20/9#

#= ((cancel9)1)/((cancel100)5) * ((cancel20)1)/((cancel9)1)#

#= (1 * 1)/(5 * 1)#

#= 1/5#

hence, #P(A) = 1/5#.

this can be checked by applying the multiplication rule again:

#P(A) * P(B) = 1/5 * 9/20 = (1 * 9)/(5 * 20) = 9/100#

#P (A and B) = 9/100#