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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 2 · Set 1 · Q14
At the start of a cricket match, a coin is tossed and the team winning the toss has the opportunity to choose to bat or bowl. Such a coin is unbiased…
At the start of a cricket match, a coin is tossed and the team winning the toss has the opportunity to choose to bat or bowl. Such a coin is unbiased with equal probabilities of getting head and tail.
Based on the above information, answer the following questions :
(a)
If such a coin is tossed $\displaystyle 2$ times, then find the probability distribution of number of tails.
(b)
Find the probability of getting at least one head in three tosses of such a coin.
Marking-scheme solution
(a)
Let $\displaystyle X$ denote the number of tails:
| $\displaystyle X$ | $\displaystyle 0$ | $\displaystyle 1$ | $\displaystyle 2$ |
| $\displaystyle P(X)$ | $\displaystyle \dfrac{1}{4}$ | $\displaystyle \dfrac{1}{2}$ | $\displaystyle \dfrac{1}{4}$ |
(b)
$\displaystyle S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
$\displaystyle P(\text{at least one head}) = 1 - P(\text{no head})$
$\displaystyle = 1 - \dfrac{1}{8}$
$\displaystyle = \dfrac{7}{8}$
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