A die is tossed. What is P(of the number being prime knowing that its even)?

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Answer 1 · 2017-03-03T08:59:24

The probability is #P(A//B)=1/3#. See explanation.

In this task we are looking for a conditional probability. We have the 2 events:

#A# - a prime number is thrown

#B# - an even number is thrown

To calculate the conditional probability we use the formula:

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

As we see in the formula we need a probability of #B# and
#AnnB#

#P(B)=3/6=1/2# because there are #3# even numbers

#P(AnnB)=1/6# because there is only one number which is prime and even (#2#)

Now we can calculate the conditional probability:

#P(A//B)=1/6-:1/2=1/6xx2/1=1/3#