Question

1.a) Roll the dice twice. What is the probability that the spot count in both dices is less than or equal to 4? (Answer is a fraction.)

1.b) Two cards are lifted from the deck so that after the first withdrawal the card is put back in and the deck is shuffled again. What is the probability that neither of the cards is a heart? (Answer is a fraction.)

1.c) Two cards are removed from the pack of cards without being put back. What is the probability that neither of the cards is a heart? (Answer is a fraction.)

1. d) The bus runs every 20 minutes. You arrive at the stop at a random moment. What is the probability that the bus will arrive in the next 4 minutes? (Answer is a fraction.)

Thank you so much! Just the answers are enough for me.

Answer 1

1a) when two dice are rolled

Total outcomes= 36

sum of less than or equal to 4 = { (1,1) (1,2) (1,3) (2,1) (2,2) (3,1) }

P( sum of leass than or equal to 4) = 6/36 = 1/6

1 b) total number of the cards = 52

total number of hearts= 13

P ( neither of the cards is hearts ) = P( first card is not a heart) * P( second card is also not a heart)

= ( 39/52) * ( 39/52)

= 9/16

1 c) P ( neither of the cards is hearts ) = P( first card is not a heart) * P( second card is also not a heart)

= (39/52) * (38/51)

= 19/34

1 d) When you reach at the bus stop, the arrival of bus for you will follow a uniform distribution in between 0 to 20 mins

X~ uniform ( 0, 20)

P( Bus will arrive in next 4 mins) = P( X < 4) =

  =  

= 4/20

= 1/5