Step 1a

Total number of cards in the deck, N = 52.
Number of heart cards, H = 13.

The probability of drawing a heart (P) is given by the ratio of the number of heart cards to the total number of cards: \$"P" = ("H"/"N")\$

Plug in the values: H = 13 and N = 52:
\$"P" = 13/52\$
\$"P" = 1/4\$

Explanation: Here we identified the Relevant Information. Here the values are substituted and simplified to the fraction. Therefore, the probability of drawing a heart from a standard deck of cards is \$1/4\$.

Step 2a

Each coin has 2 possible outcomes (heads or tails). Since there are 3 coins flipped, the total number of outcomes is \$"n"("S") = 2^3 = 8\$

We need to find the number of outcomes where exactly two heads occur. These outcomes are HHT, HTH, and THH n(E) = 3.

Explanation: Finding the total number of outcomes (n(S)) and Finding favorable outcomes (n(E)).

Step 2b

The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of outcomes.
P(Exactly two heads) = \$("n"("E"))/("n"("S"))\$

Substituting the values: P(Exactly two heads) = \$3/8\$

Explanation: Therefore, the probability of getting exactly two heads when flipping three fair coins is \$3/8\$.