NCERT Class XII Mathematics Chapter - - Solutions
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Question : 93
Total: 101
In a game, a man wins a rupee for a six and loses a rupee for any othernumber when a fair die is thrown. The man decided to throw a die thrice butto quit as and when he gets a six. Find the expected value of the amount hewins/loses.
Solution:
Probability of getting a six =
∴ q = 1 −
=
(I) Let E : the man gets a six in first throw, then P(E) =
(II) Let F : the man does not get a six in first throw, but he gets a six in the second throw, then P(F)=
×
=
(III)Let G : the man does not get a six in first two throws but he gets a six in the third throw, then P(G)=
×
×
=
(IV)Let H : the man does not get a six in any of three throws, then P(H)=
×
×
=
When man gets a six in the first throw, he gets Rs. 1.
When man gets a six in the second throw, he gets Rs.(–1 + 1) = Rs. 0
when man gets a six in the third throw, he gets Rs. (– 1 – 1 + 1) = Rs. (– 1) i.e. he loses Rs. 1.
When a man does not get any six in three throws, he gets Rs. (–1 – 1 – 1) = Rs. (–3) i.e., he loses Rs. 3.
∴ Expected value E(X)= (
) × 1 +
× 0 +
× ( − 1 ) +
× ( − 3 ) = Rs .
( loss )
(I) Let E : the man gets a six in first throw, then P(E) =
(II) Let F : the man does not get a six in first throw, but he gets a six in the second throw, then P(F)
(III)Let G : the man does not get a six in first two throws but he gets a six in the third throw, then P(G)
(IV)Let H : the man does not get a six in any of three throws, then P(H)
When man gets a six in the first throw, he gets Rs. 1.
When man gets a six in the second throw, he gets Rs.(–1 + 1) = Rs. 0
when man gets a six in the third throw, he gets Rs. (– 1 – 1 + 1) = Rs. (– 1) i.e. he loses Rs. 1.
When a man does not get any six in three throws, he gets Rs. (–1 – 1 – 1) = Rs. (–3) i.e., he loses Rs. 3.
∴ Expected value E(X)
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