A standard deck of cards has had all the face cards removed so that only the ace through 10 of each suit remains. A card is drawn from the deck and a 6-sided die is rolled. Assume the Ace has a value of 1. Determine the probability of:
a) drawing an even card (2, 4, 6, 8, or 10 of any suit) followed by an even die roll
b) drawing an Ace following by die roll of 5 or 6

Question

A standard deck of cards has had all the face cards removed so that only the ace through 10 of each suit remains. A card is drawn from the deck and a 6-sided die is rolled. Assume the Ace has a value of 1. Determine the probability of:
a) drawing an even card (2, 4, 6, 8, or 10 of any suit) followed by an even die roll
b) drawing an Ace following by die roll of 5 or 6

welshfella · Answer

total number of cards in the pack = 52 - 12 = 40
how many of these cards are even?

probability of drawing an even card =  number of even cairds / 40

welshfella · Answer

the seconf event is a roll of the die - half of the 6 numbers are even

Find these 2 probabilities and as the 2 events are independent the probability of both events occurring are the product of the 2 individual evants

welshfella · Answer

P(even card + even number on die) = P(even card)* P(even number)

welshfella · Answer

(b)  similar method

there are 4 aces in a pack of 40 
and  P( 5 or  6) = P(6) + p(5)