Francisco reaches into the bag that has 3 white marbles 3 gr

Francisco reaches into the bag that has 3 white marbles, 3 grey marbles, and 3 black marbles. He chooses one of the marbles without looking. He puts the marble and then Navaeh reaches into the bag and chooses a marble without looking. What is the probability that they both choose a black marble? A. 1/12 B. 1/9 C. 1/3 D. 7/12 Natalie has a deck of cards. What is the probability she draws an ace, puts it aside, and then draws a second ace from the deck? A. 0.0045 B. 0.0059 C. 0.0588 D. 0.0769

Solution

P(event) = No. Of Favourable outcomes/ Total no. of possible Outcomes

7) The total no. of marbles in the Bag before Francisco picks = 3+3+3 = 9 , of which there are 3 black marbles.

Therefore the probability of Francisco picking a black marble = 3/9 = 1/3

Now there are 8 marbles remaining of which 2 are black.

Therefore the probability of Navaeh picking a black marble = 2/8 = 1/4

Therefore the required Probability = 1/3 * 1/4 = 1/12 (Option A)

8) A deck of Cards has 52 cards of which there are 4 aces.

Probability of picking an ace = 4/52 = 1/13

Now there are 3 aces remaining in the deck of 51 card (as the card picked has not been replaced)

Probability of picking the second ace = 3/51 = 1/17

Therefore the required probability = 1/13 * 1*17 = 0.0045 (Option A)