Explanation:
QUESTION 1
Two coins are flipped. Find the probability that the first coin land on heads and the second coin lands on heads.
There are four possible outcomes when two coins are flipped: HH, HT, TH, and TT. Since the coins are fair, each outcome is equally likely.
The probability of the first coin landing on heads is 1/2, and the probability of the second coin landing on heads is also 1/2.
Therefore, the probability of both coins landing on heads is:
P(HH) = P(first coin lands on H) × P(second coin lands on H)
= 1/2 × 1/2
= 1/4
Hence, the probability that the first coin lands on heads and the second coin lands on heads is 1/4.
QUESTION 2
Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is black and the second card is an Ace.
There are 26 black cards in a deck of 52 cards, and there are 4 Aces in a deck of 52 cards. Since the first card is replaced before drawing the second card, the two draws are independent.
The probability of drawing a black card on the first draw is 26/52 = 1/2. The probability of drawing an Ace on the second draw is 4/52 = 1/13.
Therefore, the probability of the first card being black and the second card being an Ace is:
P(black and Ace) = P(black on first draw) × P(Ace on second draw)
= 1/2 × 1/13
= 1/26
Hence, the probability that the first card is black and the second card is an Ace is 1/26.
QUESTION 3
A single digit between 0 and 9 is randomly chosen, and a single letter from A to Z is randomly chosen. Find the probability that the number is 6 and the letter is a consonant.
There are 10 possible digits and 21 possible consonants in the English alphabet. Since the choices are independent, the probability of selecting a 6 as the digit and a consonant as the letter is the product of the probabilities of each event occurring separately.
The probability of selecting a 6 is 1/10, and the probability of selecting a consonant is 21/26.
Therefore, the probability of selecting a 6 and a consonant is:
P(6 and consonant) = P(6) × P(consonant)
= 1/10 × 21/26
= 21/260
= 3/40
Hence, the probability that the number is 6 and the letter is a consonant is 3/40.
QUESTION 4
Two dice are rolled. Find the probability that first die lands on an even number and the second die is less than 3.
There are 6 possible outcomes when two dice are rolled: (1,1), (1,2), (1,3), (2,1), (2,2), and so on. Each outcome is equally likely.
The probability of rolling an even number on the first die is 1/2, since there are three even numbers (2, 4, 6) and three odd numbers (1, 3, 5) on a standard six-sided die. The probability of rolling a number less than 3 on the second die is 2/6, since there are two numbers less than 3 (1 and 2) out of six possible outcomes.
Therefore, the probability of the first die landing on