Question

two cards are dealt in succession from a standard deck of cards. find the probability that the first card is a diamond or a king.

probability that the second card is red given that the first card was a heart.

if two dice are rolled, what is the probability of rolling at least one three?

i have 2c1(5/6)^1(1/6)^1+2c2(5/6)^1(1/6)^2 but what do i do after this. can someone please explain in regular terms, NOT math terms! thanks :)

f(x)=x+5, g(x)=x^2-2x+1
f(2)-g(2)..how do i do this????

Answer 1

The first card has a 1/4 chance of being a diamond. Since the phrase is "or," it now excludes all diamonds, including the king of diamonds. So now the chances of getting a king are 3 kings out of the remaining 39 cards. In an "either-or" situation you add the individual probabilities of the specific events.

There is a 1/4 chance of getting a heart on the first card. Without replacement, the chances of getting a red card are 25 out of the remaining 51 cards. Since you want to know the probability of "both/all" events occurring, you multiply the individual probabilities.

"At least one three" means one three or two threes. Since each die has 6 sides, the probability = 1/6 + 1/36. ("either-or" again)

I hope this helps. Thanks for asking.