Tree diagram for Example 7उदाहरण 7 का वृक्ष आरेखExample 7 ka tree diagram

NCERT Fig 13.2 · Class 12 Maths · Chapter 13 · interactive diagram

Parts and what they mean

• Start (आरंभ) — First a coin is tossed.
• First toss: 1/2 each (पहली उछाल: हर एक 1/2) — Head or tail, each with probability \tfrac{1}{2}.
• Head on first toss (पहली उछाल पर चित) — After a head, the coin is tossed again.
• Tail on first toss (पहली उछाल पर पट) — After a tail, a die is thrown.
• Second toss: 1/2 each (दूसरी उछाल: हर एक 1/2) — So P(H, H) = P(H, T) = \tfrac{1}{2} \times \tfrac{1}{2} = \tfrac{1}{4}.
• Outcome (H, H) (परिणाम (H, H)) — Probability \tfrac{1}{4}. No tail here, so it is NOT in F.
• Outcome (H, T) (परिणाम (H, T)) — Probability \tfrac{1}{4}. It has a tail, so it is in F (but no die, so not in E).
• Die outcomes (T, i) (पासे के परिणाम (T, i)) — Each (T, i) has probability \tfrac{1}{2} \times \tfrac{1}{6} = \tfrac{1}{12} — the 8 outcomes are NOT equally likely.
• E: die shows more than 4 (E: पासे पर 4 से बड़ी संख्या) — E = \{(T,5), (T,6)\}, P(E \cap F) = \tfrac{1}{6}, and P(E|F) = \dfrac{1/6}{3/4} = \dfrac{2}{9}.
• Colour key (रंग-संकेत) — F = at least one tail: P(F) = \tfrac{1}{4} + 6 \times \tfrac{1}{12} = \tfrac{3}{4}.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 13.2. Report a mistake