Question

1) The lunch special at Ann's Restaurant is a sandwich and a drink. There are 2 sandwiches and 4 drinks to choose from. How many lunch specials are possible?

2) A bag contains ten balls labeled 1 through 10. One ball will be randomly picked.
What is the probability of picking an odd number? Write your answer as a fraction in simplest form.
3) In a standard 52 card deck, What is the probability that the card drawn is a seven?
4) In a standard 52 card deck, What is the probability that the card drawn is a red card and a seven

Answer 1

1) There are 2 sandwiches and 4 drinks, so there are 2 x 4 = 8 possible lunch specials.

2) There are 5 odd numbers among the 10 balls labeled 1 through 10. Therefore, the probability of picking an odd number is:

P(odd) = number of odd balls / total number of balls = 5/10 = 1/2

So, the probability of picking an odd number is 1/2.

3) There are four sevens in a standard 52 card deck (one for each suit), so the probability of drawing a seven is:

P(seven) = number of sevens / total number of cards = 4/52 = 1/13

So, the probability of drawing a seven is 1/13.

4) There are 26 red cards in a standard 52 card deck (half of the cards are red), and four of these are sevens. Therefore, the probability of drawing a red card and a seven is:

P(red and seven) = P(red) x P(seven | red)

where P(red) is the probability of drawing a red card and P(seven | red) is the probability of drawing a seven given that a red card has been drawn.

P(red) = number of red cards / total number of cards = 26/52 = 1/2

P(seven | red) = number of red sevens / number of red cards = 4/26 = 2/13

So,

P(red and seven) = (1/2) x (2/13) = 1/13

Therefore, the probability of drawing a red card and a seven is 1/13.