Question

You randomly draw twice from this deck of cards[D] [F] [O] [B] [B] [C]What is the probability of not drawing a B, then not drawing a B replacing the first card? Write as a fraction

Answer 1

4/9

Explanation:

Answer 2

4/9

EXPLANATION

The probability of not drawing a B in each event is the same because the card is being replaced and the total number of cards is always the same. This probability is equivalent to 1 minus the probability of drawing a B,

`P(notB)=1-P(B)`

There are 6 cards in total, and 2 of them are B. Thus, the probability of not drawing a B in each event is,

`P(notB)=1-(2)/(6)=1-(1)/(3)=(2)/(3)`

The probability we want to find is the probability of not drawing a B twice in a row,

`P(notB,notB)=P(notB)\cdot P(notB)=(2)/(3)\cdot(2)/(3)=(4)/(9)`

Hence, the probability of not drawing a B, then not drawing a B is 4/9.