The chance of one event happening is the square of the chance of a 2nd event, but odds against the first are the cubes of the odds against the 2nd. Find the chances of first event. (Assume that both events are neither sure nor impossible)
A
19
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B
13
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C
23
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D
29
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Solution
The correct option is A19 Let the first event A1 and the second event A2 Let P(A1)=p2q2∴P(A2)=pq odds against second event =q−pp odds against first event =q2−p2p2 ⇒(q−pp)3=q2−p2p2 ⇒(q−p)2=(q+p)p ⇒q2=3pq⇒pq=13 ∴P(A1)=19;P(A2)=13