test yourself! practice tool\nshown are a standard deck of 52 cards and a fair coin.\nwhat is the…

test yourself! practice tool\nshown are a standard deck of 52 cards and a fair coin.\nwhat is the theoretical probability a black card is picked and the coin lands on heads? type your answer as a fraction in simplest form.

test yourself! practice tool\nshown are a standard deck of 52 cards and a fair coin.\nwhat is the theoretical probability a black card is picked and the coin lands on heads? type your answer as a fraction in simplest form.

Answer

Explanation:

Step1: Calculate probability of picking a black card

In a standard deck of 52 cards, there are 26 black cards. So the probability of picking a black card $P(B)=\frac{26}{52}=\frac{1}{2}$.

Step2: Calculate probability of coin landing on heads

A fair - coin has 2 possible outcomes (heads or tails). So the probability of getting heads $P(H)=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since the card - picking and coin - tossing are independent events, the probability of both events occurring is $P = P(B)\times P(H)$. $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$

Answer:

$\frac{1}{4}$