Question

1. what is the probability of picking a red card out of a standard deck of 52 cards, replacing it, then drawing a spade? 8) the following countries are written on pieces of paper and placed inside a hat: “cuba, jamaica, canada, america, mexico, haiti, grenada and honduras”. what is the probability of selecting a country that starts with the letter “c”, throwing it away, and then selecting “america”?

Explanation:

Problem 7

Step1: Find probability of red card

A standard deck has 26 red cards (hearts and diamonds) out of 52. So probability of red card, \( P(\text{Red}) = \frac{26}{52} = \frac{1}{2} \).

Step2: Find probability of spade

After replacing the red card, the deck is still 52 cards. There are 13 spades. So \( P(\text{Spade}) = \frac{13}{52} = \frac{1}{4} \).

Step3: Multiply the probabilities (independent events)

Since the card is replaced, the two events are independent. So \( P(\text{Red then Spade}) = P(\text{Red}) \times P(\text{Spade}) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \).

Step1: Find number of countries starting with "C"

The countries are: Cuba, Jamaica, Canada, America, Mexico, Haiti, Grenada, Honduras. Countries starting with "C": Cuba, Canada (2 countries). Total countries initially: 8. So \( P(\text{starts with C}) = \frac{2}{8} = \frac{1}{4} \).

Step2: Find probability of selecting "America" after removing one

After removing a country starting with "C", there are 7 countries left. "America" is still there. So \( P(\text{America after}) = \frac{1}{7} \).

Step3: Multiply the probabilities (dependent events)

Since we throw away the first country, the events are dependent. So \( P(\text{C then America}) = \frac{2}{8} \times \frac{1}{7} = \frac{2}{56} = \frac{1}{28} \).

Answer:

\(\frac{1}{8}\)

Problem 8