CBSE Class 10 Math Question Paper 2016 | Q20

The given question is a medium difficulty 3-mark question from the chapter Probability. The question has 3 parts one each to compute probability for a specific outcome when three different coins are tossed together. This probability question and appeared in Section C of the 2016 CBSE class 10 board paper.

Question 20: Three different coins are tossed together. Find the probability of getting
(i) exactly two heads
(ii) at least two heads
(iii) at least two tails

Video Explanation

Explanatory Answer | CBSE 2016 Maths Paper Q20

3 different coins are tossed.
Total number of possibilities = 2 × 2 × 2 = 8
The 8 outcomes are HHH, HHT, HTH, THH, TTH, THT, HTT and TTT

(i) Probability of getting exactly 2 heads

Possible outcomes HHT, HTH, THH = 3 outcomes
∴ Probability = \\frac{\text{Number of outcomes of getting exactly 2 heads}}{\text{Total number of outcomes}})
= \\frac{3}{8})

(ii) Probability of getting at least 2 heads

What does "at least 2 heads" mean?
Minimum of 2 heads. i.e., 2 heads or 3 heads
Outcomes with 2 heads or 3 heads: HHT, HTH, THH, HHH = 4 outcomes
∴ Probability = \\frac{\text{Number of outcomes of getting at least 2 heads}}{\text{Total number of outcomes}})
= \\frac{4}{8}) = \\frac{1}{2})

(iii) Probability of getting at least 2 tails

What does "at least 2 tails" mean?
Minimum of 2 tails. i.e., 2 tails or 3 tails
Outcomes with 2 tails or 3 tails: TTH, THT, HTT, TTT = 4 outcomes
∴ Probability = \\frac{\text{Number of outcomes of getting at least 2 tails}}{\text{Total number of outcomes}})
= \\frac{4}{8}) = \\frac{1}{2})