India plays two matches each with West Indies | vedclass

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(B) India plays a total of $4$ matches. The maximum points in any single match is $2$.Therefore,the maximum total points in $4$ matches is $8$.To get

Vedclass · Accepted Answer

$0.0875$

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(B) India plays a total of $4$ matches. The maximum points in any single match is $2$.Therefore,the maximum total points in $4$ matches is $8$.To get at least $7$ points,India must get either $7$ points or $8$ points.Let $X_i$ be the points in the $i$-th match,where $P(X_i=0)=0.45, P(X_i=1)=0.05, P(X_i=2)=0.50$.For a total of $8$ points,India must score $2$ points in all $4$ matches:$P(8) = (0.50)^4 = 0.0625$.For a total of $7$ points,India must score $2$ points in $3$ matches and $1$ point in $1$ match:$P(7) = \binom{4}{1} 	imes (0.50)^3 	imes (0.05)^1 = 4 	imes 0.125 	imes 0.05 = 0.0250$.The probability of getting at least $7$ points is $P(7) + P(8) = 0.0250 + 0.0625 = 0.0875$.

Outcome	$\omega_1$	$\omega_2$	$\omega_3$	$\omega_4$	$\omega_5$	$\omega_6$
$(a)$	$\frac{1}{6}$	$\frac{1}{6}$	$\frac{1}{6}$	$\frac{1}{6}$	$\frac{1}{6}$	$\frac{1}{6}$

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X = x)$	$0.15$	$0.23$	$k$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

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

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