NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question 38

Question. 38

A game: Toss a coin 3 times. If 1 or 2 heads appear, Sweta gets her entry fee back; if 3 heads appear, she gets double back; otherwise she loses. Find probabilities that she (i) loses (ii) gets double (iii) just gets entry fee back.

Answer:

(i) \(\dfrac{1}{8}\), (ii) \(\dfrac{1}{8}\), (iii) \(\dfrac{3}{4}\)

Detailed Answer with Explanation:

Step 1: When a coin is tossed 3 times, the total number of possible outcomes is:

\(2^3 = 8\) (because each toss has 2 possibilities: Head (H) or Tail (T)).

Step 2: Write all possible outcomes:

HHH, HHT, HTH, THH, HTT, THT, TTH, TTT

Step 3: Group them by number of heads:

  • 0 heads: TTT
  • 1 head: HTT, THT, TTH
  • 2 heads: HHT, HTH, THH
  • 3 heads: HHH

Step 4: Now check conditions given in the problem:

  • Sweta loses if 0 heads appear. Outcomes = 1 (TTT).
  • Sweta gets double if 3 heads appear. Outcomes = 1 (HHH).
  • Sweta gets entry fee back if 1 or 2 heads appear. Outcomes = 3 + 3 = 6.

Step 5: Find probabilities = (Number of favorable outcomes) ÷ (Total outcomes).

  • (i) Probability of losing = \(\tfrac{1}{8}\).
  • (ii) Probability of getting double = \(\tfrac{1}{8}\).
  • (iii) Probability of getting entry fee back = \(\tfrac{6}{8} = \tfrac{3}{4}\).
Open NCERT PDFOpen NCERT Answers PDF