Probability question (Bayes theorem)

Question

If H occurs, select number from 1 to 10. If T occurs, select number from 11 to 30. If selected number is prime, find the probability that it is in H.

Comments

me too getting 2 / 5

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If a no. is between 1-10, that event is H

No question states

If H occurs, select number from 1 to 10.

not the converse which you said

Also details are missing that's why i assumed it is a coin toss where H is heads and T is tails

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That's the case then

Answer 1

Event H, Selecting a Prime no from H = 4/10;   (Prime n0=  2, 3, 5,7)

Event T ,Selecting a Prime no from  T= 6/20;   (Prime No= 11,13 ,17, 19, 23,29)

probability of H or T chosen =1/2;     p =probability,   P =Prime 

Probability(H/P)={(1/2)*(4/10)}/{(1/2)*(4/10)+(1/2)*(6/20)}=(4/20)/(7/20)=4/7