Question 2)[Basic] You roll a fair ten-faced die, numbered from one to ten, then

ID: 3203325 • Letter: Q

Question

Question 2)[Basic] You roll a fair ten-faced die, numbered from one to ten, then ten you draw a card from a standard deck of 52 cards.

a) What is the size of the sample space?

b) Find P(A), A is the outcome in which you roll a 10 and then draw the Ace of spades.

c) Find the chances of you rolling a number smaller than 9 and then drawing the Ace of spades.

d) Find the chances of you rolling the number 10 and then drawing a card of spades.

e) Find the chances of you rolling a number smaller than 9 and then drawing a card of spades, or rolling anything and then drawing the ace of spades.

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I am struggling with this Econ Stat homework. Please help! Thank you :)

a) What is the size of the sample space?

There are 10 possible outcomes after rolling a 10-faced dice and there are 52 outcomes when a card is drawn from a deck of 52 cards.

Hence sample space = 10 * 52 = 520

b) Find P(A), A is the outcome in which you roll a 10 and then draw the Ace of spades.

P(A) = 1/10 * 1/52 = 1/520

c) Find the chances of you rolling a number smaller than 9 and then drawing the Ace of spades.

possible outcomes less than 9 on rolling a 10 faced dice = 8

Probability = 8/10*1/52 = 8/520 = 2/130

d) Find the chances of you rolling the number 10 and then drawing a card of spades.

Probability = 1/10 * 13/52 = 1/40

e) Find the chances of you rolling a number smaller than 9 and then drawing a card of spades, or rolling anything and then drawing the ace of spades.

Probability = 8/10*1/52 + 1 * 1/52 = 18/520 = 9/260

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