Question

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point $0,1$ and $2$ are $0.45,0.05$ and $0.50$ respectively. Assuming that the outcomes are independents, the probability of India getting at least $7$ points is

• A. $0.8750$
• B. $0.0875$
• C. $0.0625$
• D. $0.025$

Answer 1

The correct option is B

$0.0875$

Explanation of correct answer :

Finding the probability of India getting at least $7$ points :

India plays two matches each with West Indies and Australia.

i.e. Total number of matches played by India is $4$

The maximum point in any two matches is $2$

Therefore, the maximum number of points that can be gotten in four matches is: $2\times 4=8$

According to the question, we need the probability of India getting at least $7$ points.

i.e Probability of getting $7$ points as well as $8$ points is needed.

$7$points in $4$ matches is only possible when , India get $2$ points in $3$ matches while $1$point in the last match.

And for $8$points, in all match $2$ points are needed.

The required probability $=P\left(7\right)+P\left(8\right)$

$$\begin{gathered} ={}^4\mathrm{C}_3{\left(0.5\right)}^3(0.05)+{}^4\mathrm{C}_4{\left(0.5\right)}^4 \\ =0.025+0.0625 \\ =0.0875 \end{gathered}$$

Hence, the probability of India getting at least $7$ points is $0.0875$.

Therefore, the correct answer is option(B).