Question

1. A fair die is tossed twice ,find the probability of getting a 4 or 5 on the first toss and find the probability of getting 1, 2 or 3 on the second toss?
2. Diana draws a card at random deck of cards without replacing the card that she drawed , what is the probability that the first card is a 3 and a second card is a diamond ?

Answer 1

1). Probability of getting 4 or 5 on first toss and 1,2or 3 on second toss = P(4 or 5 on first)*P(1,2 or 3 on second)

[As both trials are independent to each other]

= 2/6 *3/6 = 1/6.

2). P(first is 3 and second is diamond) = ?

As there are 4 cards which have no. 3 and 13 cards are diamond out of 52 cards.

Now , there is also a one 3 diamond card.

So, P(first is 3 and second is diamond) =

P(first is 3 and diamond)*P(second is diamond|first is 3 diamond) + P(first is 3 and not diamond)*P(second is diamond | first is not diamond) = 1/52*12/51 + 3/52*13/51

= (12+39)/52*51 = 1/52