A pair of fair dice is rolled. If sum of the numbers obtained is less than 5 then a letter is chosen at random from the letters of the word DIVIDE. If the sum is more than 9 then a letter is chosen at random from the letters of the word GARDEN. Otherwise a letter is chosen at random from the letters of the word INDIAN. If probability of getting a prime score when the selected letter is a vowel is ‘p’, then the integral part of 17p is

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 7.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Let $E_{1} : sum 〈5, E_{2} : 6 \leq sum \leq 9 and E_{3} : sum〉 9$
${PE}_{1} = \frac{1 + 2 + 3}{36} = \frac{1}{6}, {PE}_{3} = \frac{1}{6} \Rightarrow {PE}_{2} = \frac{24}{36} = \frac{4}{6}$
Let E be the event of choosing a vowel. Using Baye’s theorem
$P (\frac{E_{1}}{E}) = [\frac{\frac{1}{6} \times \frac{3}{6}}{\frac{1}{6} \times \frac{3}{6} + \frac{4}{6} \times \frac{3}{6} + \frac{1}{6} \times \frac{2}{6}}] = \frac{3}{17}$
Similarly $P (E_{2} / E) = 12 / 17 and P (E_{3} / E) = 2 / 17$
Required probability
$\begin{array}{l} P = \frac{3}{17} \times (\frac{1 + 2}{6}) + \frac{12}{17} \times (\frac{4 + 6}{24}) + \frac{2}{17} \times (\frac{2}{6}) \\ 17 P = [\frac{3}{2} + 5 + \frac{2}{3}] = \frac{43}{6} \Rightarrow 17 p = 7 \end{array}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th