alleryStart learning →One card is drawn from a standard deck. What is the probability of drawing a heart or a 7?
AIt is 17/52
BIt is 1/13
CIt is 4/13
DIt is 5/13
Answer & Solution
Correct answer: C. It is 4/13
1. A standard deck holds equal numbers of hearts, diamonds, clubs and spades, so the probability of a heart is 1/4.
2. There are four 7s among 52 cards, so the probability of a 7 is 4/52 = 1/13.
3. One card, the 7 of hearts, lies in both events, so the intersection has probability 1/52.
4. Apply the union formula: 1/4 + 1/13 - 1/52.
5. Over the common denominator 52 that is 13/52 + 4/52 - 1/52 = 16/52.
6. Simplifying gives 4/13.
7. Skipping the subtraction leaves 17/52, which double counts the 7 of hearts, and that is the trap here.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.7 Probability_
Keep practising Sequences, Probability and Counting Theory
Browse all Sequences, Probability and Counting Theory questions for B.Sc Mathematics, or explore more Mathematics topics.
Related questions
A bin holds 3 bunnies, 5 dogs and 6 bears. A child picks 5 toys at random. What is the proA store has 8 phones and 3 of them are defective. A couple buys 2 phones at random. What iTwo six-sided number cubes are rolled. What is the probability that the sum is greater thaThe probability that a horse wins a race is 1/9. What is the probability that it loses?One card is drawn from a standard deck. What is the probability of drawing a heart or a spWhat makes two events mutually exclusive?When finding the probability that E or F occurs, why is the probability of E and F subtracA fair six-sided number cube is rolled. What is the probability of rolling an odd number?