JEE Main Maths – Conditional Probability explained step by step.
“Let’s first read the question carefully.” “A card is drawn from a standard deck of fifty-two cards.” “What is the probability that the card is a heart, given that it is a red card?” “We are given four options, and we’ll solve this step by step.”
“First, let’s recall basic facts about a deck of cards.” “There are fifty-two cards in total.” “Out of these, twenty-six cards are red.” “Red cards include hearts and diamonds.”
“Now pay close attention to the words ‘given that’.” “We are told that the card is red.” “This means black cards are no longer possible.” “So we completely ignore black cards.” “Only red cards remain in our sample space.”
“Among the red cards, let’s count carefully.” “There are twenty-six red cards in total.” “Out of these, thirteen cards are hearts.” “These thirteen hearts are our favourable outcomes.”
“Now we calculate the probability.” “Probability is favourable outcomes divided by total possible outcomes.” “So here, probability equals thirteen divided by twenty-six.” “When we simplify this fraction, we get one by two.”
“So the correct answer is one by two.” “Always remember this rule.” “The phrase ‘given that’ changes the sample space.” “You calculate probability inside the given condition.”
