All MCQs

There are 36 equally likely ordered outcomes.
Six outcomes have sum 7, so the probability is 6/36 = 1/6.

The equally likely outcomes are HH, HT, TH, and TT.
Exactly one head occurs in HT and TH, giving 2/4 = 1/2.

There are 4 aces among 52 cards.
Thus, the probability is 4/52 = 1/13.

A standard deck has 26 red cards out of 52 total cards.
Thus, 26/52 = 1/2.

There are six equally likely die outcomes and only one is 5.
Thus, the probability is 1/6.

A fair coin has two equally likely outcomes.
One favorable outcome out of two gives probability 1/2.

Thirty-two students study at least one subject.
Out of 40 students, 40 - 32 = 8 study neither.

Use n(M ∪ E) = n(M) + n(E) - n(M ∩ E).
Thus, 22 + 18 - 8 = 32.

A set with n elements has 2ⁿ subsets.
For n = 5, this is 2⁵ = 32.

The complement contains universal-set elements not in A.
Removing 2 and 4 leaves 1, 3, and 5.

The union contains every distinct element from either set.
Thus, A ∪ B = {1, 2, 3}.

The intersection contains elements common to both sets.
Only 3 appears in both A and B.