Question

1. the probability of choosing a face card from a deck of cards is (\frac{3}{13}). the probability of tossing heads on a coin is (\frac{1}{2}). what is the probability of choosing a face card from a deck of cards and tossing heads on a coin at the same time? a (\frac{7}{26}) b (\frac{19}{26}) c (\frac{3}{26}) d (\frac{4}{15})

Explanation:

Step1: Identify independent events

Choosing a face card and tossing a coin are independent events. The probability of two independent events \( A \) and \( B \) occurring together is \( P(A \cap B)=P(A)\times P(B) \).
Let \( A \) be the event of choosing a face card (\( P(A)=\frac{3}{13} \)) and \( B \) be the event of tossing heads (\( P(B)=\frac{1}{2} \)).

Step2: Calculate the combined probability

Multiply the probabilities of the two events:
\[
P(A\cap B)=\frac{3}{13}\times\frac{1}{2}=\frac{3}{26}
\]

Answer:

C. \(\frac{3}{26}\)