Question

7) * Loretta does not return the first card.10 pointsLoretta wrote one letter of her name on each of 7 note cards, as shown below.Ll|of|R|ET|TJALoretta shuffled the cards and turned them upside down so she could not see the letters.She chose 2 cards, one at a time. What is the probability that Loretta chosc an O firstand a T second?A } CÀB1 DRA BBOD

Answer 1

probability of an event = (required outcome) / (total possible outcome)

Also if two events A and B are independent,

P(AnB) = P(A) x P(B)

In this case,

total possible outcome = 7 (Since there are 7 cards)

The number of cards marked 'O' is 1.

So the probability of picking 'O' first = 1 / 7

After picking O and not putting it back,

total possible outcome = 7 - 1 =6

and the number of Ts remain 2

So the probability of picking T second = 2 / 6 = 1 / 3

The probability of picking O first is independent of the probability of picking T second

Hence,

The probability of picking O first and T second is

`(1)/(3)*(1)/(7)=(1)/(21)`