Question

calculate the following probabilities.

1. calculate the probability of drawing a king from

the deck followed by another king, if the first
card is replaced after it is drawn.

1. calculate the probability of rolling a 3 on a die

followed by another 3 on the same die.

1. a bag contains 5 red marbles and 4 blue marbles.

calculate the probability of drawing a red marble
followed by a blue marble if the first marble is
not replaced after it is drawn.

1. find the probability of a family having a girl

followed by another girl two years later.

1. find the probability of rolling a 4 on a die and

getting a heads when a coin is flipped.

1. calculate the probability of drawing a three from

a deck and then drawing another three from the
same deck if the first card is not replaced.

Explanation:

Question 7

Step1: Determine probability of first king

A standard deck has 52 cards, 4 kings. Probability of drawing a king: $\frac{4}{52}=\frac{1}{13}$.

Step2: Determine probability of second king (with replacement)

Since the first card is replaced, the deck remains 52 cards. Probability of drawing a king again: $\frac{4}{52}=\frac{1}{13}$.

Step3: Multiply the probabilities

For independent events, $P(A\cap B)=P(A)\times P(B)$. So $\frac{1}{13}\times\frac{1}{13}=\frac{1}{169}$.

Step1: Probability of first 3

A die has 6 faces. Probability of rolling a 3: $\frac{1}{6}$.

Step2: Probability of second 3 (independent)

Rolling a die is independent. Probability of rolling a 3 again: $\frac{1}{6}$.

Step3: Multiply probabilities

$P = \frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Step1: Probability of red marble

Total marbles: $5 + 4 = 9$. Probability of red: $\frac{5}{9}$.

Step2: Probability of blue marble (no replacement)

After drawing a red, 8 marbles left, 4 blue. Probability of blue: $\frac{4}{8}=\frac{1}{2}$.

Step3: Multiply probabilities

$P=\frac{5}{9}\times\frac{1}{2}=\frac{5}{18}$.

Answer:

$\frac{1}{169}$

Question 8