You select a card at random from the cards that make up the word “replacement”. Without replacing the card, you choose a second card. Find the probability of choosing a consonant and then an “e”. There is 1 letter for each card.

Question

anonymous · Answer

On the first card, the probability of drawing a consonant is the number of consonants divided by the total number of letters.  There are 7 consonants (r, p, l, c, m, n, t), and 11 total letters.  So the probability of drawing a consonant on the first draw is 7/11.

The first card is not replaced, so on the 2nd draw, there are only 10 remaining cards.  The chance of drawing an "e" is the number of "e" cards (which is 2) divided by the total remaining cards, or 2/10 which is 1/5.

The probability of BOTH events occurring is the product:  (7/11) * (1/5)

anonymous · Answer

Does that make sense?  You just count up how many ways you can "win" (get the criteria they are asking about) and divide by the total number of ways to "play".

If there are two conditions that must BOTH happen to be a "win" overall, then the overall probability is the product of the two individual probabilities.